Maximal Regularity of Fully Discrete Finite Element Solutions of Parabolic Equations
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.
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© 2017, Society for Industrial and Applied Mathematics.
History
Submitted: 22 April 2016
Accepted: 9 December 2016
Published online: 7 March 2017
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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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