Discrete maximal parabolic regularity for galerkin finite element methods for nonautonomous parabolic problems

Dmitriy Leykekhman; Boris Vexler

doi:10.1137/17M114100X

Discrete maximal parabolic regularity for galerkin finite element methods for nonautonomous parabolic problems

Dmitriy Leykekhman, Boris Vexler

Chair of Optimal Control

University of Connecticut

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

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 (0, ; ²(Ω)) norm for 1 ≤ ≤ ∞.

Original language	English
Pages (from-to)	2178-2202
Number of pages	25
Journal	SIAM Journal on Numerical Analysis
Volume	56
Issue number	4
DOIs	https://doi.org/10.1137/17M114100X
State	Published - 2018

Keywords

Discontinuous Galerkin methods
Discrete maximal parabolic regularity
Finite elements
Maximal parabolic regularity
Nonautonomous problems
Optimal error estimates
Parabolic problems
Time-dependent coefficients

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10.1137/17M114100X

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title = "Discrete maximal parabolic regularity for galerkin finite element methods for nonautonomous parabolic problems",

abstract = "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 (0, ; 2(Ω)) norm for 1 ≤ ≤ ∞.",

keywords = "Discontinuous Galerkin methods, Discrete maximal parabolic regularity, Finite elements, Maximal parabolic regularity, Nonautonomous problems, Optimal error estimates, Parabolic problems, Time-dependent coefficients",

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KW - Discontinuous Galerkin methods

KW - Discrete maximal parabolic regularity

KW - Finite elements

KW - Maximal parabolic regularity

KW - Nonautonomous problems

KW - Optimal error estimates

KW - Parabolic problems

KW - Time-dependent coefficients

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JF - SIAM Journal on Numerical Analysis

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ER -

Discrete maximal parabolic regularity for galerkin finite element methods for nonautonomous parabolic problems

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Keywords

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