Moving Mesh Methods for Implicit Moving Boundary Problems

Abstract

This talk will present a method for achieving arbitrarily high orders of accuracy when approximating PDE-based moving boundary problems using finite element (and related) methods on moving computational meshes. Its effectiveness will be demonstrated on a nonlinear diffusion problem for which the boundary velocity is only defined implicitly as part of the PDE problem. In this situation high-order approximations can be achieved for both the movement of the boundary and the update of the evolving solution on the moving mesh.

Document