Parabolic finite volume element equations in nonconvex polygonal domains

P. Chatzipantelidis; R.D. Lazarov; V. Thomée

doi:10.1002/num.20351

journal article Open Access May 13, 2008

Parabolic finite volume element equations in nonconvex polygonal domains

P. Chatzipantelidis R.D. Lazarov V. Thomée

Numerical Methods for Partial Differential Equations Vol. 25 No. 3 pp. 507-525 · Wiley

View at Publisher Save 10.1002/num.20351

Abstract

AbstractWe study spatially semidiscrete and fully discrete finite volume element approximations of the heat equation with homogeneous Dirichlet boundary conditions in a plane polygonal domain with one reentrant corner. We show that, as a result of the singularity in the solution near the reentrant corner, the convergence rate is reduced from optimal second order, similarly to what was shown for the finite element method in the earlier work 2. Optimal order convergence may be restored by mesh refinement near the corners of the domain. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009

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References

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Error estimates for a finite volume element method for parabolic equations in convex polygonal domains

P. Chatzipantelidis, R. D. Lazarov, V. Thomée

Numerical Methods for Partial Differential Equatio... 10.1002/num.20006

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Details

Published: May 13, 2008
Vol/Issue: 25(3)
Pages: 507-525
License: View

Authors

Cite This Article

P. Chatzipantelidis, R.D. Lazarov, V. Thomée (2008). Parabolic finite volume element equations in nonconvex polygonal domains. Numerical Methods for Partial Differential Equations, 25(3), 507-525. https://doi.org/10.1002/num.20351

Parabolic finite volume element equations in nonconvex polygonal domains

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