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

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页码：2307 / 2325

页数：19

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