Moving Mesh Method with Conservative Interpolation Based on L^2-Projection (Communications in Computational Physics, 2006)
We develop an efficient one-dimensional moving mesh algorithm for solving partial differential equations. The main contribution of this paper is to design aneffective interpolation scheme based on L2-projection for the moving mesh method.The proposed method preserves not only the mass-conservation but also the first ordermomentum of the underlying numerical solution at each mesh redistribution step. Numerical examples are presented to demonstrate the effectiveness of the new interpolationtechnique.