Numerical methods for changing type systems
arXiv:1610.08824 · doi:10.1093/imanum/dry007
Abstract
In this note we develop a numerical method for partial differential equations with changing type. Our method is based on a unified solution theory found by Rainer Picard for several linear equations from mathematical physics. Parallel to the solution theory already developed, we frame our numerical method in a discontinuous Galerkin approach in space-time with certain exponentially weighted spaces.
Extended version with more details and an additional example, including appendix "On the weighted Gauß--Radau Quadrature" (see arXiv:1610.09016)