Moving Mesh Method with Conservative Interpolation Based on L^2-Projection

Abstract

We develop an efficient one-dimensional moving mesh algorithm for solving partial differential equations. The main contribution of this paper is to design an effective interpolation scheme based on L²-projection for the moving mesh method. The proposed method preserves not only the mass-conservation but also the first order momentum of the underlying numerical solution at each mesh redistribution step. Numerical examples are presented to demonstrate the effectiveness of the new interpolation technique.