Resolvent estimates and numerical implementation for the homogenisation of one-dimensional periodic mixed type problems
Provides a numerical scheme for a class of homogenisation problems with mixed type, but the contribution is incremental as it applies existing methods to a specific problem setting.
The authors develop a homogenisation framework for one-dimensional periodic mixed-type problems with highly oscillatory coefficients, and implement a discontinuous Galerkin method in time with continuous Galerkin in space for numerical treatment. The method is validated through numerical experiments showing convergence.
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.