Vlasák, Miloslav, Kučera, Václav
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We deal with a nonstationary semilinear singularly perturbed convection–diffusion problem. We discretize this problem by discontinuous Galerkin method in space and by midpoint rule in time. We present diffusion–uniform error estimates with sketches of proofs.
U. Risch, G. Lube (1990)
Banach Center Publications
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Balázsová, Monika, Feistauer, Miloslav, Hadrava, Martin, Kosík, Adam
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This paper is concerned with the stability analysis of the space-time discontinuous Galerkin method for the solution of nonstationary, nonlinear, convection-diffusion problems. In the formulation of the numerical scheme we use the nonsymmetric, symmetric and incomplete versions of the discretization of diffusion terms and interior and boundary penalty. Then error estimates are briefly characterized. The main attention is paid to the investigation of unconditional stability of the method....
Paola Causin, Riccardo Sacco, Carlo L. Bottasso (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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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...
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...
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...