Página 1 dos resultados de 96 itens digitais encontrados em 0.020 segundos

Um estimador de erro a posteriori para a equação do transporte de contaminantes em regime de pequena advecção; A posteriori error estimate for the contaminant transport equation in small advection regime

Jesus, Alessandro Firmiano de
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Tese de Doutorado Formato: application/pdf
Publicado em 19/03/2010 Português
Relevância na Pesquisa
936.689%
Vários modelos computacionais que implementam o transporte de soluto em meio poroso saturado surgem constantemente em publicações científicas devido à suma importância dada à compreensão e previsão do transporte de constituintes dissolvidos em água subterrânea. As soluções numéricas obtidas por esquemas computacionais não estão imunes aos erros de discretização. No entanto, a confiabilidade nos resultados obtidos das complexas operações provenientes da dinâmica de fluidos computacional pode ser aumentada através de estimadores de erro a posteriori que indicam a precisão da solução numérica de um modelo matemático que simula o fenômeno físico de interesse. Neste trabalho é apresentado um estimador residual para a equação parabólica que descreve os fenômenos de advecção-dispersão-reação (ADR) em meio poroso saturado, considerando o transporte em regime de pequena advecção. A solução numérica da equação ADR é obtida pelo método dos elementos finitos que emprega termos upwind para minimizar as inconvenientes oscilações espúrias. A implementação do código computacional para obter essa solução numérica e o seu correspondente erro a posteriori, é feita em linguagem JAVA na plataforma Eclipse seguindo o paradigma da Programação Orientada a Objetos (POO). A solução numérica da equação elíptica do fluxo subterrâneo e o seu estimador de erro com características de recuperação do gradiente...

Estimador de erro a posteriori baseado em recuperação do gradiente para o método dos elementos finitos generalizados; A posteriori error estimator based on gradient recovery for the generalized finite element method

Lins, Rafael Marques
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Dissertação de Mestrado Formato: application/pdf
Publicado em 11/05/2011 Português
Relevância na Pesquisa
1027.4173%
O trabalho aborda a questão das estimativas a posteriori dos erros de discretização e particularmente a recuperação dos gradientes de soluções numéricas obtidas com o método dos elementos finitos (MEF) e com o método dos elementos finitos generalizados (MEFG). Inicialmente, apresenta-se, em relação ao MEF, um resumido estado da arte e conceitos fundamentais sobre este tema. Em seguida, descrevem-se os estimadores propostos para o MEF denominados Estimador Z e "Superconvergent Patch Recovery" (SPR). No âmbito do MEF propõe-se de modo original a incorporação do "Singular Value Decomposition" (SVD) ao SPR aqui mencionada como SPR Modificado. Já no contexto do MEFG, apresenta-se um novo estimador do erro intitulado EPMEFG, estendendo-se para aquele método as idéias do SPR Modificado. No EPMEFG, a função polinomial local que permite recuperar os valores nodais dos gradientes da solução tem por suporte nuvens (conjunto de elementos finitos que dividem um nó comum) e resulta da aplicação de um critério de aproximação por mínimos quadrados em relação aos pontos de superconvergência. O número destes pontos é definido a partir de uma análise em cada elemento que compõe a nuvem, considerando-se o grau da aproximação local do campo de deslocamentos enriquecidos. Exemplos numéricos elaborados com elementos lineares triangulares e quadrilaterais são resolvidos com o Estimador Z...

A COMPUTATIONAL MEASURE THEORETIC APPROACH TO INVERSE SENSITIVITY PROBLEMS II: A POSTERIORI ERROR ANALYSIS*

BUTLER, T.; ESTEP, D.; SANDELIN, J.
Fonte: PubMed Publicador: PubMed
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
805.93086%
In part one of this paper [T. Butler and D. Estep, SIAM J. Numer. Anal., to appear], we develop and analyze a numerical method to solve a probabilistic inverse sensitivity analysis problem for a smooth deterministic map assuming that the map can be evaluated exactly. In this paper, we treat the situation in which the output of the map is determined implicitly and is difficult and/or expensive to evaluate, e.g., requiring the solution of a differential equation, and hence the output of the map is approximated numerically. The main goal is an a posteriori error estimate that can be used to evaluate the accuracy of the computed distribution solving the inverse problem, taking into account all sources of statistical and numerical deterministic errors. We present a general analysis for the method and then apply the analysis to the case of a map determined by the solution of an initial value problem.

Operator-adapted finite element wavelets : theory and applications to a posteriori error estimation and adaptive computational modeling

Sudarshan, Raghunathan, 1978-
Fonte: Massachusetts Institute of Technology Publicador: Massachusetts Institute of Technology
Tipo: Tese de Doutorado Formato: 171 leaves; 7377914 bytes; 7399145 bytes; application/pdf; application/pdf
Português
Relevância na Pesquisa
727.2734%
We propose a simple and unified approach for a posteriori error estimation and adaptive mesh refinement in finite element analysis using multiresolution signal processing principles. Given a sequence of nested discretizations of a domain we begin by constructing approximation spaces at each level of discretization spanned by conforming finite element interpolation functions. The solution to the virtual work equation can then be expressed as a telescopic sum consisting of the solution on the coarsest mesh along with a sequence of error terms denoted as two-level errors. These error terms are the projections of the solution onto complementary spaces that are scale-orthogonal with respect to the inner product induced by the weak-form of the governing differential operator. The problem of generating a compact, yet accurate representation of the solution then reduces to that of generating a compact, yet accurate representation of each of these error components. This problem is solved in three steps: (a) we first efficiently construct a set of scale-orthogonal wavelets that form a Riesz stable basis (in the energy-norm) for the complementary spaces; (b) we then efficiently estimate the contribution of each wavelet to the two-level error and finally (c) we select a subset of the wavelets at each level to preserve and solve exactly for the corresponding coefficients. Our approach has several advantages over a posteriori error estimation and adaptive refinement techniques in vogue in finite element analysis. First...

A mixed finite element method for the generalized Stokes problem

González Taboada, María; Bustinza, Rommel; Gatica, Gabriel N.
Fonte: John Wiley & Sons Ltd. Publicador: John Wiley & Sons Ltd.
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
1025.00305%
[Abstract] We present and analyse a new mixed finite element method for the generalized Stokes problem. The approach, which is a natural extension of a previous procedure applied to quasi-Newtonian Stokes flows, is based on the introduction of the flux and the tensor gradient of the velocity as further unknowns. This yields a two-fold saddle point operator equation as the resulting variational formulation. Then, applying a slight generalization of the well known Babuška–Brezzi theory, we prove that the continuous and discrete formulations are well posed, and derive the associated a priori error analysis. In particular, the finite element subspaces providing stability coincide with those employed for the usual Stokes flows except for one of them that needs to be suitably enriched. We also develop an a posteriori error estimate (based on local problems) and propose the associated adaptive algorithm to compute the finite element solutions. Several numerical results illustrate the performance of the method and its capability to localize boundary layers, inner layers, and singularities.

A low-order mixed finite element method for a class of quasi-Newtonian Stokes flows. Part II: a posteriori error analysis

González Taboada, María; Gatica, Gabriel N.; Meddahi, Salim
Fonte: Elsevier BV Publicador: Elsevier BV
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
1017.6314%
[Abstract] This is the second part of a work dealing with a low-order mixed finite element method for a class of nonlinear Stokes models arising in quasi-Newtonian fluids. In the first part we showed that the resulting variational formulation is given by a twofold saddle point operator equation, and that the corresponding Galerkin scheme becomes well posed with piecewise constant functions and Raviart–Thomas spaces of lowest order as the associated finite element subspaces. In this paper we develop a Bank–Weiser type a posteriori error analysis yielding a reliable estimate and propose the corresponding adaptive algorithm to compute the mixed finite element solutions. Several numerical results illustrating the efficiency of the method are also provided.

A Posteriori Error Estimates of Krylov Subspace Approximations to Matrix Functions

Jia, Zhongxiao; Lv, Hui
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
729.78766%
Krylov subspace methods for approximating a matrix function $f(A)$ times a vector $v$ are analyzed in this paper. For the Arnoldi approximation to $e^{-\tau A}v$, two reliable a posteriori error estimates are derived from the new bounds and generalized error expansion we establish. One of them is similar to the residual norm of an approximate solution of the linear system, and the other one is determined critically by the first term of the error expansion of the Arnoldi approximation to $e^{-\tau A}v$ due to Saad. We prove that each of the two estimates is reliable to measure the true error norm, and the second one theoretically justifies an empirical claim by Saad. In the paper, by introducing certain functions $\phi_k(z)$ defined recursively by the given function $f(z)$ for certain nodes, we obtain the error expansion of the Krylov-like approximation for $f(z)$ sufficiently smooth, which generalizes Saad's result on the Arnoldi approximation to $e^{-\tau A}v$. Similarly, it is shown that the first term of the generalized error expansion can be used as a reliable a posteriori estimate for the Krylov-like approximation to some other matrix functions times $v$. Numerical examples are reported to demonstrate the effectiveness of the a posteriori error estimates for the Krylov-like approximations to $e^{-\tau A}v$...

Functional A Posteriori Error Equalities for Conforming Mixed Approximations of Elliptic Problems

Anjam, Immanuel; Pauly, Dirk
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 11/03/2014 Português
Relevância na Pesquisa
838.65516%
In this paper we show how to find the exact error (not just an estimate of the error) of a conforming mixed approximation by using the functional type a posteriori error estimates in the spirit of Repin. The error is measured in a mixed norm which takes into account both the primal and dual variables. We derive this result for elliptic partial differential equations of a certain class. We first derive a special version of our main result by using a simplified reaction-diffusion problem to demonstrate the strong connection to the classical functional a posteriori error estimates of Repin. After this we derive the main result in an abstract setting. Our main result states that in order to obtain the exact global error value of a conforming mixed approximation one only needs the problem data and the mixed approximation of the exact solution. There is no need for calculating any auxiliary data. The calculation of the exact error consists of simply calculating two (usually integral) quantities where all the quantities are known after the approximate solution has been obtained by any conforming method. We also show some numerical computations to confirm the results.; Comment: key words: functional a posteriori error estimate, error equality...

A Posteriori Error Control for the Binary Mumford-Shah Model

Berkels, Benjamin; Effland, Alexander; Rumpf, Martin
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 20/05/2015 Português
Relevância na Pesquisa
729.9602%
The binary Mumford-Shah model is a widespread tool for image segmentation and can be considered as a basic model in shape optimization with a broad range of applications in computer vision, ranging from basic segmentation and labeling to object reconstruction. This paper presents robust a posteriori error estimates for a natural error quantity, namely the area of the non properly segmented region. To this end, a suitable strictly convex and non-constrained relaxation of the originally non-convex functional is investigated and Repin's functional approach for a posteriori error estimation is used to control the numerical error for the relaxed problem in the $L^2$-norm. In combination with a suitable cut out argument, a fully practical estimate for the area mismatch is derived. This estimate is incorporated in an adaptive meshing strategy. Two different adaptive primal-dual finite element schemes, and the most frequently used finite difference discretization are investigated and compared. Numerical experiments show qualitative and quantitative properties of the estimates and demonstrate their usefulness in practical applications.; Comment: 18 pages, 7 figures, 1 table

Residual-based a posteriori error estimation for multipoint flux mixed finite element methods

Du, Shaohong; Sun, Shuyu; Xie, Xiaoping
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 22/12/2013 Português
Relevância na Pesquisa
721.8702%
A novel residual-type {\it a posteriori} error analysis technique is developed for multipoint flux mixed finite element methods for flow in porous media in two or three space dimensions. The derived {\it a posteriori} error estimator for the velocity and pressure error in $L^{2}-$norm consists of discretization and quadrature indicators, and is shown to be reliable and efficient. The main tools of analysis are a locally postprocessed approximation to the pressure solution of an auxiliary problem and a quadrature error estimate. Numerical experiments are presented to illustrate the competitive behavior of the estimator.

A posteriori error estimates for continuous/discontinuous Galerkin approximations of the Kirchhoff-Love buckling problem

Hansbo, Peter; Larson, Mats G.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 02/02/2015 Português
Relevância na Pesquisa
810.1087%
Second order buckling theory involves a one-way coupled coupled problem where the stress tensor from a plane stress problem appears in an eigenvalue problem for the fourth order Kirchhoff plate. In this paper we present an a posteriori error estimate for the critical buckling load and mode corresponding to the smallest eigenvalue and associated eigenvector. A particular feature of the analysis is that we take the effect of approximate computation of the stress tensor and also provide an error indicator for the plane stress problem. The Kirchhoff plate is discretized using a continuous/discontinuous finite element method which uses standard continuous piecewise polynomial finite element spaces which can also be used to solve the plane stress problem.

A-posteriori error estimates for inverse problems

Rao, Vishwas; Sandu, Adrian
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
725.4367%
Inverse problems use physical measurements along with a computational model to estimate the parameters or state of a system of interest. Errors in measurements and uncertainties in the computational model lead to inaccurate estimates. This work develops a methodology to estimate the impact of different errors on the variational solutions of inverse problems. The focus is on time evolving systems described by ordinary differential equations, and on a particular class of inverse problems, namely, data assimilation. The computational algorithm uses first-order and second-order adjoint models. In a deterministic setting the methodology provides a posteriori error estimates for the inverse solution. In a probabilistic setting it provides an a posteriori quantification of uncertainty in the inverse solution, given the uncertainties in the model and data. Numerical experiments with the shallow water equations in spherical coordinates illustrate the use of the proposed error estimation machinery in both deterministic and probabilistic settings.; Comment: Contains a total of 51 pages

A posteriori error estimates for discontinuous Galerkin method to the elasticity problem

Luong, Thi Hong Cam; Daveau, Christian
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 10/06/2015 Português
Relevância na Pesquisa
722.9224%
This work concerns with the discontinuous Galerkin (DG)method for the time-dependent linear elasticity problem. We derive the a posteriori error bounds for semi-discrete and fully discrete problems, by making use of the stationary elasticity reconstruction technique which allows to estimate the error for time-dependent problem through the error estimation of the associated stationary elasticity problem. To this end, to derive the error bound for the stationary problem, we present two methods to obtain two different a posteriori error bounds, by $L^2$ duality technique and via energy norm. For fully discrete scheme, we make use of the backward-Euler scheme and an appropriate space-time reconstruction. The technique here can be applicable for a variety of DG methods as well.; Comment: 31 pages, conference: WAVE 2015-Germany

Verification of functional a posteriori error estimates for obstacle problem in 2D

Harasim, Petr; Valdman, Jan
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 26/03/2014 Português
Relevância na Pesquisa
810.1934%
We verify functional a posteriori error estimate proposed by S. Repin for a class of obstacle problems. The obstacle problem is formulated as a quadratic minimization problem with constrains equivalently formulated as a variational inequality. New benchmarks with known analytical solutions in 2D are constructed based on 1D benchmark introduced by P. Harasim and J. Valdman. Numerical approximation of the obstacle problem is obtained by the finite element method using bilinear elements on a rectangular mesh. Error of the approximation is meassured in the energy norm and bounded from above by a functional majorant, whose value is minimized with respect to unknown gradient field discretized by Raviart-Thomas elements and Lagrange multipliers field discretized by piecewise constant functions.; Comment: 20 pages, 13 figure

A-posteriori error estimates for the localized reduced basis multi-scale method

Ohlberger, Mario; Schindler, Felix
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
817.4977%
We present a localized a-posteriori error estimate for the localized reduced basis multi-scale (LRBMS) method [Albrecht, Haasdonk, Kaulmann, Ohlberger (2012): The localized reduced basis multiscale method]. The LRBMS is a combination of numerical multi-scale methods and model reduction using reduced basis methods to efficiently reduce the computational complexity of parametric multi-scale problems with respect to the multi-scale parameter $\varepsilon$ and the online parameter $\mu$ simultaneously. We formulate the LRBMS based on a generalization of the SWIPDG discretization presented in [Ern, Stephansen, Vohralik (2010): Guaranteed and robust discontinuous Galerkin a posteriori error estimates for convection-diffusion-reaction problems] on a coarse partition of the domain that allows for any suitable discretization on the fine triangulation inside each coarse grid element. The estimator is based on the idea of a conforming reconstruction of the discrete diffusive flux, that can be computed using local information only. It is offline/online decomposable and can thus be efficiently used in the context of model reduction.

A posteriori error estimates for the Electric Field Integral Equation on polyhedra

Nochetto, Ricardo H.; Stamm, Benjamin
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 17/04/2012 Português
Relevância na Pesquisa
813.56836%
We present a residual-based a posteriori error estimate for the Electric Field Integral Equation (EFIE) on a bounded polyhedron. The EFIE is a variational equation formulated in a negative order Sobolev space on the surface of the polyhedron. We express the estimate in terms of square-integrable and thus computable quantities and derive global lower and upper bounds (up to oscillation terms).; Comment: Submitted to Mathematics of Computation

A Posteriori Error Analysis of $hp$-FEM for singularly perturbed problems

Melenk, Jens M.; Wihler, Thomas P.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
809.6125%
We consider the approximation of singularly perturbed linear second-order boundary value problems by $hp$-finite element methods. In particular, we include the case where the associated differential operator may not be coercive. Within this setting we derive an a posteriori error estimate for a natural residual norm. The error bound is robust with respect to the perturbation parameter and fully explicit with respect to both the local mesh size $h$ and the polynomial degree $p$.

A Posteriori Error Estimates for Energy-Based Quasicontinuum Approximations of a Periodic Chain

Wang, Hao
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 22/12/2011 Português
Relevância na Pesquisa
736.3476%
We present a posteriori error estimates for a recently developed atomistic/continuum coupling method, the Consistent Energy-Based QC Coupling method. The error estimate of the deformation gradient combines a residual estimate and an a posteriori stability analysis. The residual is decomposed into the residual due to the approximation of the stored energy and that due to the approximation of the external force, and are bounded in negative Sobolev norms. In addition, the error estimate of the total energy using the error estimate of the deformation gradient is also presented. Finally, numerical experiments are provided to illustrate our analysis.

Verification of functional a posteriori error estimates for obstacle problem in 1D

Harasim, Petr; Valdman, Jan
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
826.4697%
We verify functional a posteriori error estimate for obstacle problem proposed by Repin. Simpli?cation into 1D allows for the construction of a nonlinear benchmark for which an exact solution of the obstacle problem can be derived. Quality of a numerical approximation obtained by the ?nite element method is compared with the exact solution and the error of approximation is bounded from above by a majorant error estimate. The sharpness of the majorant error estimate is discussed.

Functional a posteriori error estimate for a nonsymmetric stationary diffusion problem

Mali, Olli
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 21/11/2014 Português
Relevância na Pesquisa
824.4877%
In this paper, a posteriori error estimates of functional type for a stationary diffusion problem with nonsymmetric coefficients are derived. The estimate is guaranteed and does not depend on any particular numerical method. An algorithm for the global minimization of the error estimate with respect to the flux over some finite dimensional subspace is presented. In numerical tests, global minimization is done over the subspace generated by Raviart-Thomas elements. The improvement of the error bound due to the p-refinement of these spaces is investigated.; Comment: 8 pages