Uniform convergent tailored finite point method for advection-diffusion equation with discontinuous, anisotropic and vanishing diffusivity
The authors propose the two tailored finite point method for numerical approximation of solutions to steady state advection-diffusion equations with discontinuous, vanishing diffusivity. The first method deals with the case when the diffusion is aligned with the coordinates, while the second one is concerned with general nonaligned tensor diffusivity. The diffusion tensor and advection coefficient are approximated by piecewise constants which allows to locally express the solution by a linear combination of special solutions to the constant coefficient equations. The authors obtain uniform convergence of the proposed algorithms in the vanishing diffusivity limit, even when the solution exhibits interface and boundary layers. In case when the diffusivity is along the coordinates, it is shown that the positivity and maximum principle hold.
steady state advection-diffusion equation
scientific article; zbMATH DE number 6690803
scientific article