๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

A posteriori error analysis for linearization of nonlinear elliptic problems and their discretizations

โœ Scribed by Weimin Han

Publisher
John Wiley and Sons
Year
1994
Tongue
English
Weight
826 KB
Volume
17
Category
Article
ISSN
0170-4214

No coin nor oath required. For personal study only.

โœฆ Synopsis

Abstract

The paper is devoted to a posteriori quantitative analysis for errors caused by linearization of nonโ€linear elliptic boundary value problems and their finite element realizations. We employ duality theory in convex analysis to derive computable bounds on the difference between the solution of a nonโ€linear problem and the solution of the linearized problem, by using the solution of the linearized problem only. We also derive computable bounds on differences between finite element solutions of the nonlinear problem and finite element solutions of the linearized problem, by using finite element solutions of the linearized problem only. Numerical experiments show that our a posteriori error bounds are efficient.

๐Ÿ“œ SIMILAR VOLUMES

A posteriori error estimates for variabl
A posteriori error estimates for variable time-step discretizations of nonlinear evolution equations
โœ Ricardo H. Nochetto; Giuseppe Savarรฉ; Claudio Verdi ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 336 KB ๐Ÿ‘ 2 views

We study the backward Euler method with variable time steps for abstract evolution equations in Hilbert spaces. Exploiting convexity of the underlying potential or the angle-bounded condition, thereby assuming no further regularity, we derive novel a posteriori estimates of the discretization error

A posteriori error estimates for nonline
A posteriori error estimates for nonlinear problems: Lr, (0, T; W1,ฯ (ฮฉ))-error estimates for finite element discretizations of parabolic equations
โœ R. Verfรผrth ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 546 KB

Using the abstract framework of [R. Verfรผrth, Math. Comput. 62, 445-475 (1996)], we analyze a residual a posteriori error estimator for space-time finite element discretizations of parabolic PDEs. The estimator gives global upper and local lower bounds on the error of the numerical solution. The fin

Functional a posteriori error estimates
Functional a posteriori error estimates for discontinuous Galerkin approximations of elliptic problems
โœ Raytcho Lazarov; Sergey Repin; Satyendra K. Tomar ๐Ÿ“‚ Article ๐Ÿ“… 2009 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 261 KB

## Abstract In this article, we develop functional a posteriori error estimates for discontinuous Galerkin (DG) approximations of elliptic boundaryโ€value problems. These estimates are based on a certain projection of DG approximations to the respective energy space and functional a posteriori estim