Parabolic Finite Volume Element Equations in Nonconvex Polygonal Domains Academic Article

abstract

• We 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 []. Optimal order convergence may be restored by mesh refinement near the corners of the domain. 2008 Wiley Periodicals, Inc.

authors

• Lazarov, Raytcho

published proceedings

• NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS

author list (cited authors)

• Chatzipantelidis, P., Lazarov, R. D., & Thomee, V.

citation count

• 17

complete list of authors

• Chatzipantelidis, P||Lazarov, RD||Thomee, V

publication date

• May 2009

publisher

• Wiley  Publisher

published in

• Numerical Methods for Partial Differential Equations  Journal

keywords

• Convergence Rate
• Error Estimates
• Finite Volume Element Method
• Nanconvex Polygonal Domain
• Parabolic Equations

Digital Object Identifier (DOI)

• 10.1002/num.20351

start page

• 507

end page

• 525

volume

• 25

issue

• 3

URL

• http%3A%2F%2Fdx.doi.org%2F10.1002%2Fnum.20351