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| In this paper, a new moving mesh finite volume method is presented for time dependent diffusion equations. In the proposed method, the mesh moving procedure is replaced with the mesh optimization based on centroidal Voronoi tessellation. The new method can avoid some problems arising from the classic moving mesh methods such as expensive computations cost for searching the locations of new nodes and meshes tangling in the moving process. Moreover, the Delaunay triangulation generated by CVT technology satisfies empty circle property and maximize minimum angle, which is of good quality. Finally, some numerical examples show that the new method is effective and has good accuracy and stability. |
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| Keywords:Computational Mathematics, Finite Volume Method, Centroidal Voronoi Tessellation, Moving Mesh, a Posteriori Error Estimates, Time Dependent Diffusion Equation |
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