DISCRETE MAXIMAL PARABOLIC REGULARITY FOR GALERKIN FINITE ELEMENT METHODS FOR NONAUTONOMOUS PARABOLIC PROBLEMS

被引：8

作者：

Leykekhman, Dmitriy ^{[1
]}

Vexler, Boris ^{[2
]}

机构：

[1] Univ Connecticut, Dept Math, Storrs, CT 06269 USA

[2] Tech Univ Munich, Chair Optimal Control, Ctr Math Sci, D-85748 Garching, Germany

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2018年 / 56卷 / 04期

基金：

美国国家科学基金会;

关键词：

parabolic problems; maximal parabolic regularity; discrete maximal parabolic regularity; finite elements; discontinuous Galerkin methods; optimal error estimates; time-dependent coefficients; nonautonomous problems; TIME-DEPENDENT COEFFICIENTS; POINTWISE STATE CONSTRAINTS; CRANK-NICOLSON SCHEME; SMOOTHING PROPERTY; EQUATIONS; DISCRETIZATIONS; STABILITY; OPERATORS; SPACES;

D O I：

10.1137/17M114100X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The main goal of the paper is to establish time semidiscrete and space-time fully discrete maximal parabolic regularity for the lowest order time discontinuous Galerkin solution of linear parabolic equations with time-dependent coefficients. Such estimates have many applications. As one of the applications we establish best approximations type results with respect to the L-P(O, T; L-2(Omega)) norm for 1 <= p <= infinity.

引用

页码：2178 / 2202

页数：25

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