Displaying similar documents to “A priori diffusion-uniform error estimates for singularly perturbed problems: Midpoint-DG discretization”

A local projection stabilization finite element method with nonlinear crosswind diffusion for convection-diffusion-reaction equations

Gabriel R. Barrenechea, Volker John, Petr Knobloch (2013)

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

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An extension of the local projection stabilization (LPS) finite element method for convection-diffusion-reaction equations is presented and analyzed, both in the steady-state and the transient setting. In addition to the standard LPS method, a nonlinear crosswind diffusion term is introduced that accounts for the reduction of spurious oscillations. The existence of a solution can be proved and, depending on the choice of the stabilization parameter, also its uniqueness. Error estimates...

Mesh Refinement For Stabilized Convection Diffusion Equations

B. Achchab, M. El Fatini, A. Souissi (2010)

Mathematical Modelling of Natural Phenomena

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We derive a residual a posteriori error estimates for the subscales stabilization of convection diffusion equation. The estimator yields upper bound on the error which is global and lower bound that is local

Error estimates for a FitzHugh–Nagumo parameter-dependent reaction-diffusion system

Konstantinos Chrysafinos, Sotirios P. Filopoulos, Theodosios K. Papathanasiou (2013)

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

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Space-time approximations of the FitzHugh–Nagumo system of coupled semi-linear parabolic PDEs are examined. The schemes under consideration are discontinuous in time but conforming in space and of arbitrary order. Stability estimates are presented in the natural energy norms and at arbitrary times, under minimal regularity assumptions. Space-time error estimates of arbitrary order are derived, provided that the natural parabolic regularity is present. Various physical parameters appearing...

Error estimates for a FitzHugh–Nagumo parameter-dependent reaction-diffusion system

Konstantinos Chrysafinos, Sotirios P. Filopoulos, Theodosios K. Papathanasiou (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

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Space-time approximations of the FitzHugh–Nagumo system of coupled semi-linear parabolic PDEs are examined. The schemes under consideration are discontinuous in time but conforming in space and of arbitrary order. Stability estimates are presented in the natural energy norms and at arbitrary times, under minimal regularity assumptions. Space-time error estimates of arbitrary order are derived, provided that the natural parabolic regularity...

An Adaptive Multi-level method for Convection Diffusion Problems

Martine Marion, Adeline Mollard (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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In this article we introduce an adaptive multi-level method in space and time for convection diffusion problems. The scheme is based on a multi-level spatial splitting and the use of different time-steps. The temporal discretization relies on the characteristics method. We derive an error estimate and design a corresponding adaptive algorithm. The efficiency of the multi-level method is illustrated by numerical experiments, in particular for a convection-dominated problem. ...