OPTIMAL ERROR ESTIMATES FOR FULLY DISCRETE GALERKIN APPROXIMATIONS OF SEMILINEAR PARABOLIC EQUATIONS

被引：13

作者：

Meidner, Dominik ^{[1
]}

Vexler, Boris ^{[1
]}

机构：

[1] Tech Univ Munich, Dept Math, Chair Optimal Control, Garching, Germany

来源：

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE | 2019年 / 52卷 / 06期

关键词：

Parabolic semilinear equations; finite elements; Galerkin time discretization; error estimates; FINITE-ELEMENT-METHOD; POINTWISE; REGULARITY; DISCRETIZATIONS; PRINCIPLE;

D O I：

10.1051/m2an/2018040

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a semilinear parabolic equation with a large class of nonlinearities without any growth conditions. We discretize the problem with a discontinuous Galerkin scheme dG(0) in time (which is a variant of the implicit Euler scheme) and with conforming finite elements in space. The main contribution of this paper is the proof of the uniform boundedness of the discrete solution. This allows us to obtain optimal error estimates with respect to various norms.

引用

页码：2307 / 2325

页数：19

共 50 条

[1] Nonsmooth data error estimates for fully discrete finite element approximations of semilinear parabolic equations in Banach space
Wang, Wansheng
Li, Jinping
Jin, Chengyu
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2024, 448
[2] INTERIOR ERROR-ESTIMATES FOR SEMI-DISCRETE GALERKIN APPROXIMATIONS FOR PARABOLIC EQUATIONS
NITSCHE, JA
[J]. RAIRO-ANALYSE NUMERIQUE-NUMERICAL ANALYSIS, 1981, 15 (02): : 171 - 176
[3] Error estimates for discontinuous galerkin approximations of implicit parabolic equations
Chrysafinos, K
Walkington, NJ
[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 2006, 43 (06) : 2478 - 2499
[4] A PRIORI L2 ERROR-ESTIMATES FOR GALERKIN APPROXIMATIONS TO SEMILINEAR PARABOLIC INTEGRODIFFERENTIAL EQUATIONS
LIN, YP
[J]. TRANSPORT THEORY, INVARIANT IMBEDDING, AND INTEGRAL EQUATIONS: PROCEEDINGS IN HONOR OF G M WINGS 65TH BIRTHDAY, 1989, 115 : 421 - 424
[5] A posteriori error estimates for fully discrete fractional-step υ-approximations for parabolic equations
Karakatsani, Fotini
[J]. IMA JOURNAL OF NUMERICAL ANALYSIS, 2016, 36 (03) : 1334 - 1361
[6] ERROR-ESTIMATES FOR SPATIALLY DISCRETE APPROXIMATIONS OF SEMILINEAR PARABOLIC EQUATIONS WITH NONSMOOTH INITIAL DATA
JOHNSON, C
LARSSON, S
THOMEE, V
WAHLBIN, LB
[J]. MATHEMATICS OF COMPUTATION, 1987, 49 (180) : 331 - 357
[7] ELLIPTIC RECONSTRUCTION AND A POSTERIORI ERROR ESTIMATES FOR FULLY DISCRETE SEMILINEAR PARABOLIC OPTIMAL CONTROL PROBLEMS
Manohar, Ram
Sinha, Rajen Kumar
[J]. JOURNAL OF COMPUTATIONAL MATHEMATICS, 2022, 40 (02) : 147 - 176
[8] ON FULLY DISCRETE GALERKIN APPROXIMATIONS FOR PARTIAL INTEGRODIFFERENTIAL EQUATIONS OF PARABOLIC TYPE
ZHANG, NY
[J]. MATHEMATICS OF COMPUTATION, 1993, 60 (201) : 133 - 166
[9] ERROR-ESTIMATES FOR SPATIALLY DISCRETE APPROXIMATIONS OF SEMILINEAR PARABOLIC EQUATIONS WITH INITIAL DATA OF LOW REGULARITY
CROUZEIX, M
THOMEE, V
WAHLBIN, LB
[J]. MATHEMATICS OF COMPUTATION, 1989, 53 (187) : 25 - 41
[10] SYMMETRIC ERROR ESTIMATES FOR DISCONTINUOUS GALERKIN APPROXIMATIONS FOR AN OPTIMAL CONTROL PROBLEM ASSOCIATED TO SEMILINEAR PARABOLIC PDE'S
Chrysafinos, Konstantinos
Karatzas, Efthimios N.
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2012, 17 (05): : 1473 - 1506

← 1 2 3 4 5 →