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arXiv · 2310.01237

Fitted finite element methods for singularly perturbed elliptic problems of convection-diffusion type

Alan F. Hegarty·Eugene O'Riordan
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Abstract

Fitted finite element methods are constructed for a singularly perturbed convection-diffusion problem in two space dimensions. Exponential splines as basis functions are combined with Shishkin meshes to obtain a stable parameter-uniform numerical method. These schemes satisfy a discrete maximum principle. In the classical case, the numerical approximations converge, in the maximum pointwise norm, at a rate of second order and the approximations converge at a rate of first order for all values of the singular perturbation parameter.

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Alan F. Hegarty, Eugene O'Riordan. 2023-10-02. Fitted finite element methods for singularly perturbed elliptic problems of convection-diffusion type. https://arxiv.org/abs/2310.01237

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