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Error estimates for finite element approximations of parabolic equations with measure data

Author: Wei Gong
Journal: Math. Comp. 82 (2013), 69-98
MSC (2010): Primary 49J20, 49K20, 65N15, 65N30
Published electronically: August 8, 2012
MathSciNet review: 2983016
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Abstract: In this paper we study the a priori error estimates for the finite element approximations of parabolic equations with measure data, especially we consider problems with separate measure data in time and space, respectively. The solutions of these kinds of problems exhibit low regularities due to the existence of measure data, this introduces some difficulties in both theoretical and numerical analysis. For both cases we use standard piecewise linear and continuous finite elements for the space discretization and derive the a priori error estimates for the semi-discretization problems, while the backward Euler method is then used for time discretization and a priori error estimates for the fully discrete problems are also derived. Numerical results are provided at the end of the paper to confirm our theoretical findings.

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Additional Information

Wei Gong
Affiliation: Schwerpunkt Optimierung und Approximation, Universität Hamburg, Bundesstrasse 55, 20146, Hamburg, Germany
Address at time of publication: LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

Keywords: Finite element method, parabolic equation, measure data, semi-discrete error estimates, fully discrete error estimates.
Received by editor(s): February 5, 2011
Received by editor(s) in revised form: August 8, 2011, and September 13, 2011
Published electronically: August 8, 2012
Additional Notes: This work was partially supported by the National Natural Science Foundation of China under grant 11171337 and the National Basic Research Program of China under grant 2012CB821204
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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