The space-time finite element method for parabolic problems

被引：16

作者：

Li, H ^{[1
]}

Liu, RX ^{[1
]}

机构：

[1] Univ Sci & Technol China, Dept Math, Hefei 230026, Peoples R China

来源：

APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION | 2001年 / 22卷 / 06期

关键词：

semi-linear parabolic equations; space-time finite element method; existence and uniquess; error estimate;

D O I：

10.1023/A:1016314405090

中图分类号：

O29 [应用数学];

学科分类号：

070104 [应用数学];

摘要：

Adaptive space-time finite element method, continuous in space but discontinuous in time for semi-linear parabolic problems is discussed. The approach is based on a combination of finite element and finite difference techniques. The existence and uniqueness of the weak solution are proved without any assumptions on choice of the spacetime meshes. Basic error estimates in L-infinity (L-2) norm, that is maximum-norm in time, L-2-norm in space are obtained. The numerical results are given in the last part and the analysis between theoretic and experimental results are obtained.

引用

页码：687 / 700

页数：14

共 7 条

[1]

Brenner S. C., 2007, Texts Appl. Math., V15

[2]

CIARLET P. G., 1978, The Finite Element Method for Elliptic Problems

[3]

ADAPTIVE FINITE-ELEMENT METHODS FOR PARABOLIC PROBLEMS .1. A LINEAR-MODEL PROBLEM [J].