Displaying similar documents to “Convergence rate of a finite volume scheme for the linear convection-diffusion equation on locally refined meshes”

Flux-upwind stabilization of the discontinuous Petrov–Galerkin formulation with Lagrange multipliers for advection-diffusion problems

Paola Causin, Riccardo Sacco, Carlo L. Bottasso (2005)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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In this work we consider the dual-primal Discontinuous Petrov–Galerkin (DPG) method for the advection-diffusion model problem. Since in the DPG method both mixed internal variables are discontinuous, a static condensation procedure can be carried out, leading to a single-field nonconforming discretization scheme. For this latter formulation, we propose a flux-upwind stabilization technique to deal with the advection-dominated case. The resulting scheme is conservative and satisfies a...

A continuous finite element method with face penalty to approximate Friedrichs' systems

Erik Burman, Alexandre Ern (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

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A continuous finite element method to approximate Friedrichs' systems is proposed and analyzed. Stability is achieved by penalizing the jumps across mesh interfaces of the normal derivative of some components of the discrete solution. The convergence analysis leads to optimal convergence rates in the graph norm and suboptimal of order ½ convergence rates in the -norm. A variant of the method specialized to Friedrichs' systems associated with elliptic PDE's in mixed...

Finite element methods on non-conforming grids by penalizing the matching constraint

Eric Boillat (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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The present paper deals with a finite element approximation of partial differential equations when the domain is decomposed into sub-domains which are meshed independently. The method we obtain is never conforming because the continuity constraints on the boundary of the sub-domains are not imposed strongly but only penalized. We derive a selection rule for the penalty parameter which ensures a quasi-optimal convergence.

Mimetic finite differences for elliptic problems

Franco Brezzi, Annalisa Buffa, Konstantin Lipnikov (2009)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We developed a mimetic finite difference method for solving elliptic equations with tensor coefficients on polyhedral meshes. The first-order convergence estimates in a mesh-dependent H 1 norm are derived.