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A posteriori error estimation for the discrete duality finite volume discretization of the Laplace equation

Abstract : An efficient and fully computable a posteriori error bound is derived for the discrete duality finite volume discretization of the Laplace equation on very general twodimensional meshes. The main ingredients are the equivalence of this method with a finite element like scheme and tools from the finite element framework. Numerical tests are performed with a stiff solution on highly nonconforming locally refined meshes and with a singular solution on triangular meshes.
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Submitted on : Thursday, June 4, 2009 - 11:06:18 AM
Last modification on : Tuesday, October 20, 2020 - 3:56:35 PM
Long-term archiving on: : Wednesday, September 22, 2010 - 12:39:01 PM

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Pascal Omnes, Yohan Penel, Yann Rosenbaum. A posteriori error estimation for the discrete duality finite volume discretization of the Laplace equation. SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2009, 47 (4), pp.2782--2807. ⟨10.1137/080735047⟩. ⟨cea-00320486v2⟩

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