Moving Mesh Method with Conservative Interpolation Based on L2-Projection
Zhengru Zhang 1*1 School of Mathematical Sciences, Beijing Normal University, Beijing 100875, P.R. China.
Received 1 June 2005; Accepted (in revised version) 17 September 2005
Communicated by Chi-Wang Shu
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 $L^2$-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.
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Key words: Moving mesh method; conservative interpolation; $L^2$-projection.
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Correspondence to: Zhengru Zhang , School of Mathematical Sciences, Beijing Normal University, Beijing 100875, P.R. China. Email: firstname.lastname@example.org