Multi-algorithmic methods for coupled hyperbolic-parabolic problems

We study computational methods for linear, degenerate advectiondiffusion equations leading to coupled hyperbolic-parabolic problems. A multialgorithmic 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+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.