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Fitted finite element methods for singularly perturbed elliptic problems of convection-diffusion type (2310.01237v1)
Published 2 Oct 2023 in math.NA and cs.NA
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.