[图书][B] Finite elements II
A Ern, JL Guermond - 2021 - Springer
The mathematization of all sciences, the fading of traditional scientific boundaries, the
impact of computer technology, the growing importance of computer modelling and the …
impact of computer technology, the growing importance of computer modelling and the …
[图书][B] Mathematical aspects of discontinuous Galerkin methods
DA Di Pietro, A Ern - 2011 - books.google.com
This book introduces the basic ideas to build discontinuous Galerkin methods and, at the
same time, incorporates several recent mathematical developments. The presentation is to a …
same time, incorporates several recent mathematical developments. The presentation is to a …
[图书][B] Robust numerical methods for singularly perturbed differential equations
HG Roos - 2008 - Springer
The analysis of singular perturbed differential equations began early in the twentieth
century, when approximate solutions were constructed from asymptotic expansions …
century, when approximate solutions were constructed from asymptotic expansions …
Polynomial-degree-robust a posteriori estimates in a unified setting for conforming, nonconforming, discontinuous Galerkin, and mixed discretizations
A Ern, M Vohralík - SIAM Journal on Numerical Analysis, 2015 - SIAM
We present equilibrated flux a posteriori error estimates in a unified setting for conforming,
nonconforming, discontinuous Galerkin, and mixed finite element discretizations of the two …
nonconforming, discontinuous Galerkin, and mixed finite element discretizations of the two …
[HTML][HTML] Guaranteed and robust discontinuous Galerkin a posteriori error estimates for convection–diffusion–reaction problems
A Ern, AF Stephansen, M Vohralík - Journal of computational and applied …, 2010 - Elsevier
We propose and study a posteriori error estimates for convection–diffusion–reaction
problems with inhomogeneous and anisotropic diffusion approximated by weighted interior …
problems with inhomogeneous and anisotropic diffusion approximated by weighted interior …
An introductory review on a posteriori error estimation in finite element computations
L Chamoin, F Legoll - SIAM Review, 2023 - SIAM
This article is a review of basic concepts and tools devoted to a posteriori error estimation for
problems solved with the finite element method. For the sake of simplicity and clarity, we …
problems solved with the finite element method. For the sake of simplicity and clarity, we …
A review of some a posteriori error estimates for adaptive finite element methods
K Segeth - Mathematics and Computers in Simulation, 2010 - Elsevier
Recently, the adaptive finite element methods have gained a very important position among
numerical procedures for solving ordinary as well as partial differential equations arising …
numerical procedures for solving ordinary as well as partial differential equations arising …
A posteriori error estimates including algebraic error and stopping criteria for iterative solvers
For the finite volume discretization of a second-order elliptic model problem, we derive a
posteriori error estimates which take into account an inexact solution of the associated linear …
posteriori error estimates which take into account an inexact solution of the associated linear …
Error control for the localized reduced basis multiscale method with adaptive on-line enrichment
M Ohlberger, F Schindler - SIAM Journal on Scientific Computing, 2015 - SIAM
In this contribution we consider localized, robust, and efficient a posteriori error estimation of
the localized reduced basis multiscale (LRBMS) method for parametric elliptic problems with …
the localized reduced basis multiscale (LRBMS) method for parametric elliptic problems with …
Guaranteed and robust a posteriori error estimates and balancing discretization and linearization errors for monotone nonlinear problems
L El Alaoui, A Ern, M Vohralík - Computer Methods in Applied Mechanics …, 2011 - Elsevier
We derive a posteriori error estimates for a class of second-order monotone quasi-linear
diffusion-type problems approximated by piecewise affine, continuous finite elements. Our …
diffusion-type problems approximated by piecewise affine, continuous finite elements. Our …