Numerical analysis of quasilinear parabolic equations under low regularity assumptions

被引：6

作者：

Casas, Eduardo ^{[1
]}

Chrysafinos, Konstantinos ^{[2
,3
]}

机构：

[1] Univ Cantabria, Dept Matemat Aplicada & Ciencias Comp, ETSI Ind & Telecomunicac, Av Castros S-N, E-39005 Santander, Spain

[2] Natl Tech Univ Athens, Dept Math, Sch Appl Math & Phys Sci, Zografou Campus, Athens 15780, Greece

[3] FORTH, IACM, Iraklion 20013, Crete, Greece

来源：

NUMERISCHE MATHEMATIK | 2019年 / 143卷 / 04期

关键词：

FINITE-ELEMENT APPROXIMATION; L-INFINITY-CONVERGENCE; GALERKIN APPROXIMATIONS; MAXIMAL REGULARITY;

D O I：

10.1007/s00211-019-01071-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we carry out the numerical analysis of a class of quasilinear parabolic equations, where the diffusion coefficient depends on the solution of the partial differential equation. The goal is to prove error estimates for the fully discrete equation using discontinuous Galerkin discretization in time DG(0) combined with piecewise linear finite elements in space. This analysis is performed under minimal regularity assumptions on the data. In particular, we omit any assumption regarding existence of a second derivative in time of the solution.

引用

页码：749 / 780

页数：32

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