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A posteriori error estimates for mixed finite element approximations of parabolic problems
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2011 (English)In: Numerische Mathematik, ISSN 0029-599X, E-ISSN 0945-3245, Vol. 118, no 1, 33-48 p.Article in journal (Refereed) Published
Abstract [en]

We derive residual based a posteriori error estimates for parabolic problems on mixed form solved using Raviart-Thomas-Nedelec finite elements in space and backward Euler in time. The error norm considered is the flux part of the energy, i.e. weighted L (2)(Omega) norm integrated over time. In order to get an optimal order bound, an elementwise computable post-processed approximation of the scalar variable needs to be used. This is a common technique used for elliptic problems. The final bound consists of terms, capturing the spatial discretization error and the time discretization error and can be used to drive an adaptive algorithm.

Place, publisher, year, edition, pages
2011. Vol. 118, no 1, 33-48 p.
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URN: urn:nbn:se:umu:diva-104453DOI: 10.1007/s00211-010-0328-1ISI: 000289442100002OAI: diva2:823793
Available from: 2015-06-18 Created: 2015-06-11 Last updated: 2015-06-18Bibliographically approved

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Larson, Mats G.
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Department of Mathematics and Mathematical Statistics
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