Structure preserving methods based on finite difference methods with unstructured Voronoi meshes

点击翻译按钮获取中文摘要

We have evaluated some mathematical features of finite difference operators with various error orders based on some Voronoi meshes in bounded domains and have studied error evaluations of them on nonsymmetric meshes. We also applied our methods to concrete partial differential equations, such as the Cahn-Hilliard equation, and obtained results that confirm our estimations. To decrease computation cost for those compromised numerical schemes, moreover, we have developed fast schemes based on predictor-corrector method with relaxed discrete variational derivative method and this attempt was a quite success.We have also attended and given talks on some international conferences in this three years, for example, we gave a invited talk at the SciCADE 2011.