Resolvent estimates and numerical implementation for the homogenisation of one-dimensional periodic mixed type problems

TL;DR

This paper investigates homogenisation of one-dimensional mixed type problems with oscillatory type changes, employing numerical methods like discontinuous Galerkin in time and continuous Galerkin in space.

Contribution

It introduces a homogenisation framework for oscillatory mixed type problems and implements a numerical scheme combining discontinuous and continuous Galerkin methods.

Findings

Effective homogenisation approach for oscillatory mixed type problems

Numerical scheme successfully applied to complex problems

Potential for improved computational efficiency in homogenisation

Abstract

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.