Abstract

We establish the maximal $\ell^p$-regularity for fully discrete finite element solutions of parabolic equations with time-dependent Lipschitz continuous coefficients. The analysis is based on a discrete $\ell^p(W^{1,q})$ estimate together with a duality argument and a perturbation method. Optimal-order error estimates of fully discrete finite element solutions in the norm of $\ell^p(L^q)$ follows immediately.

Keywords

  1. nonlinear parabolic equations
  2. BDF methods
  3. discrete maximal parabolic regularity
  4. maximum-norm error analysis
  5. energy technique
  6. time-dependent norms

MSC codes

  1. Primary
  2. 65M12
  3. 65M60; Secondary
  4. 65L06

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Information & Authors

Information

Published In

cover image SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Pages: 521 - 542
ISSN (online): 1095-7170

History

Submitted: 22 April 2016
Accepted: 9 December 2016
Published online: 7 March 2017

Keywords

  1. nonlinear parabolic equations
  2. BDF methods
  3. discrete maximal parabolic regularity
  4. maximum-norm error analysis
  5. energy technique
  6. time-dependent norms

MSC codes

  1. Primary
  2. 65M12
  3. 65M60; Secondary
  4. 65L06

Authors

Affiliations

Funding Information

Alexander von Humboldt-Stiftung http://dx.doi.org/10.13039/100005156
National Natural Science Foundation of China http://dx.doi.org/10.13039/501100001809 : NSFC 11301262
Research Grants Council, University Grants Committee http://dx.doi.org/10.13039/501100002920 : CityU 11302915

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