Multi-Algorithmic Methods for Coupled Hyperbolic-Parabolic Problems

Abstract

We study computational methods for linear, degenerate advection-diffusion equations leading to coupled hyperbolic-parabolic problems. A multi-algorithmic approach is proposed in which a different approximation method is used locally depending on the mathematical nature of the problem. Our analysis focuses on stability and a priori error estimates of coupled continuous and discontinuous Galerkin methods, achieving a global $h^{p+\frac{1}{2}}$ estimate. Both the mathematical analysis and the numerical results demonstrate that careful consideration is necessary when defining appropriate interface conditions between the hyperbolic and parabolic regions.