NANov 8, 2016
Numerical methods for changing type systemsSebastian Franz, Sascha Trostorff, Marcus Waurick
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.
APNov 23, 2017
Resolvent estimates and numerical implementation for the homogenisation of one-dimensional periodic mixed type problemsSebastian Franz, Marcus Waurick
We study a homogenisation problem for problems of mixed type in the framework of evolutionary equations. The change of type is highly oscillatory. The numerical treatment is done by a discontinuous Galerkin method in time and a continuous Galerkin method in space.
HOOct 25, 2016
On the weighted Gauß--Radau QuadratureSascha Trostorff, Marcus Waurick
In this short note, we collect some facts on the weighted Gauß--Radau quadrature. In particular, we focus on the location of the Gauß--Radau points being a continuous function of the $L^1$-weighting function.
NAOct 2, 2018
Homogenisation of parabolic/hyperbolic mediaSebastian Franz, Marcus Waurick
We consider an evolutionary problem with rapidly oscillating coefficients. This causes the problem to change frequently between a parabolic and an hyperbolic state. We prove convergence of the homogenisation process in the unit square and present a numerical method to deal with approximations of the resulting equations. A numerical study finalises the contribution.