A posteriori error estimates for time-dependent reaction-diffusionproblems based on the Payne--Weinberger inequality

Svetlana Matculevich; Pekka Neittaanmäki; Sergey Repin

doi:10.3934/dcds.2015.35.2659

Article Contents

2015, Volume 35, Issue 6: 2659-2677. Doi: 10.3934/dcds.2015.35.2659

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A posteriori error estimates for time-dependent reaction-diffusion problems based on the Payne--Weinberger inequality

1.
Dept. of Mathematical Information Technology, Faculty of Information Technology, C321.4, Agora, P.O. Box 35, FI-40014, University of Jyväskylä
2.
Dept. of Mathematical Information Technology, Faculty of Information Technology, Agora, P.O. Box 35, FI-40014, University of Jyväskylä

Received: January 2014

Revised: April 2014

Published: May 2017

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Abstract

We consider evolutionary reaction-diffusion problems with mixed Dirichlet--Robin boundary conditions. For this class of problems, we derive two-sided estimates of the distance between any function in the admissible energy space and the exact solution of the problem. The estimates (majorants and minorants) are explicitly computable and do not contain unknown functions or constants. Moreover, it is proved that the estimates are equivalent to the energy norm of the deviation from the exact solution.

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Mathematics Subject Classification: 35K20, 65M15, 65N30.

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