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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Maximal $L^p$ analysis of finite element solutions for parabolic equations with nonsmooth coefficients in convex polyhedra
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by Buyang Li and Weiwei Sun PDF
Math. Comp. 86 (2017), 1071-1102 Request permission

Abstract:

The paper is concerned with Galerkin finite element solutions of parabolic equations in a convex polygon or polyhedron with a diffusion coefficient in $W^{1,N+\alpha }$ for some $\alpha >0$, where $N$ denotes the dimension of the domain. We prove the analyticity of the semigroup generated by the discrete elliptic operator, the discrete maximal $L^p$ regularity and the optimal $L^p$ error estimate of the finite element solution for the parabolic equation.
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Additional Information
  • Buyang Li
  • Affiliation: Mathematisches Institut, Universität Tübingen, D-72076 Tübingen, Germany – and – Department of Mathematics, Nanjing University, Nanjing 210093, People’s Republic of China
  • Address at time of publication: Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong
  • MR Author ID: 910552
  • Email: buyang.li@polyu.edu.hk
  • Weiwei Sun
  • Affiliation: Department of Mathematics, City University of Hong Kong, Hong Kong
  • Email: maweiw@math.cityu.edu.hk
  • Received by editor(s): January 13, 2015
  • Received by editor(s) in revised form: October 19, 2015
  • Published electronically: August 18, 2016
  • Additional Notes: The work of the first author was supported in part by NSFC (grant no. 11301262), and the research stay of the author at Universität Tübingen was supported by the Alexander von Humboldt Foundation
    The work of the second author was supported in part by a grant from the Research Grants Council of the Hong Kong SAR, China (project no. CityU 11302915)
  • © Copyright 2016 American Mathematical Society
  • Journal: Math. Comp. 86 (2017), 1071-1102
  • MSC (2010): Primary 65M12, 65M60; Secondary 35K20
  • DOI: https://doi.org/10.1090/mcom/3133
  • MathSciNet review: 3614012