A parameter robust Petrov---Galerkin scheme for advection---diffusion---reaction equations

Authors:
Carlo Falco;Eugene O'Riordan
Affiliations:
Institute for Applied Mathematics and Information Technology (IMATI) CNR, Pavia, Italy;School of Mathematical Sciences, Dublin City University, Dublin, Ireland 9
Venue:
Numerical Algorithms
Year:
2011

Citing 4
Cited 0

A conservative uniformly accurate difference method for a singular perturbation problem in conservation form

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The streamline-diffusion method for a convection-diffusion problem with a point source

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Singularly perturbed convection-diffusion problems with boundary and weak interior layers

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Global maximum norm parameter-uniform numerical method for a singularly perturbed convection-diffusion problem with discontinuous convection coefficient

Mathematical and Computer Modelling: An International Journal

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Abstract

In this paper, a singularly perturbed convection diffusion boundary value problem, with discontinuous diffusion coefficient is examined. In addition to the presence of boundary layers, strong and weak interior layers can also be present due to the discontinuities in the diffusion coefficient. A priori layer adapted piecewise uniform meshes are used to resolve any layers present in the solution. Using a Petrov---Galerkin finite element formulation, a fitted finite difference operator is shown to produce numerical approximations on this fitted mesh, which are uniformly second order (up to logarithmic terms) globally convergent in the pointwise maximum norm.