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

10 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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T1 - Discrete maximal parabolic regularity for galerkin finite element methods for nonautonomous parabolic problems

AU - Leykekhman, Dmitriy

AU - Vexler, Boris

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N2 - 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 ≤ ≤ ∞.

AB - 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 ≤ ≤ ∞.

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

UR - https://www.scopus.com/pages/publications/85053548156

U2 - 10.1137/17M114100X

DO - 10.1137/17M114100X

M3 - Article

AN - SCOPUS:85053548156

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VL - 56

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EP - 2202

JO - SIAM Journal on Numerical Analysis

JF - SIAM Journal on Numerical Analysis

IS - 4

ER -

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

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Keywords

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