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 $L^p(0,T;L^2(\Omega))$ norm for $1\le p\le \infty$.

Keywords

  1. parabolic problems
  2. maximal parabolic regularity
  3. discrete maximal parabolic regularity
  4. finite elements
  5. discontinuous Galerkin methods
  6. optimal error estimates
  7. time-dependent coefficients
  8. nonautonomous problems

MSC codes

  1. 65N30
  2. 65N15

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Information & Authors

Information

Published In

cover image SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Pages: 2178 - 2202
ISSN (online): 1095-7170

History

Submitted: 27 July 2017
Accepted: 16 May 2018
Published online: 19 July 2018

Keywords

  1. parabolic problems
  2. maximal parabolic regularity
  3. discrete maximal parabolic regularity
  4. finite elements
  5. discontinuous Galerkin methods
  6. optimal error estimates
  7. time-dependent coefficients
  8. nonautonomous problems

MSC codes

  1. 65N30
  2. 65N15

Authors

Affiliations

Funding Information

National Science Foundation https://doi.org/10.13039/100000001 : DMS-1115288

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