Some properties of the discontinuous Galerkin method for one-dimensional singularly perturbed problems.
Roos, Hans-Görg, Zarin, Helena (2003)
Novi Sad Journal of Mathematics
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Roos, Hans-Görg, Zarin, Helena (2003)
Novi Sad Journal of Mathematics
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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...
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...
Gert Lube (1994)
Banach Center Publications
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In this paper, we analyze a class of stabilized finite element formulations used in computation of (i) second order elliptic boundary value problems (diffusion-convection-reaction model) and (ii) the Navier-Stokes problem (incompressible flow model). These stabilization techniques prevent numerical instabilities that might be generated by dominant convection/reaction terms in (i), (ii) or by inappropriate combinations of velocity/pressure interpolation functions in (ii). Stability and...
Teresa Regińska (1988)
Aplikace matematiky
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A pointwise error estimate and an estimate in norm are obtained for a class of external methods approximating boundary value problems. Dependence of a superconvergence phenomenon on the external approximation method is studied. In this general framework, superconvergence at the knot points for piecewise polynomial external methods is established.