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Convergence of Finite Volume Scheme for a Three-Dimensional Poisson Equation
Chalmers University of Technology and the University of Gothenburg.
Uppsala universitet, Tillämpad matematik och statistik.
2014 (English)In: Journal of Mathematical Sciences, ISSN 1072-3374, E-ISSN 1573-8795, Vol. 202, no 2, p. 130-153Article in journal (Refereed) Published
Abstract [en]

We construct and analyze a finite volume scheme for numerical solution of a three-dimensional Poisson equation. We derive optimal convergence rates in the discrete H1 norm and sub-optimal convergence in the maximum norm, where we use the maximal available regularity of the exact solution and minimal smoothness requirement on the source term. The theoretical results are justified through implementing some canonical examples in 3D.

Place, publisher, year, edition, pages
Springer-Verlag New York, 2014. Vol. 202, no 2, p. 130-153
National Category
Mathematical Analysis Computational Mathematics
Research subject
Mathematics with specialization in Applied Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-140864DOI: 10.1007/s10958-014-2038-1OAI: oai:DiVA.org:liu-140864DiVA, id: diva2:1140950
Available from: 2014-11-12 Created: 2017-09-13 Last updated: 2017-09-13Bibliographically approved

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Bartoszek, Krzysztof
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