Wavelets and adaptive grids for the discontinuous Galerkin method
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- 作者：Jorge L. D铆az Calle ; Philippe R. B. Devloo and S么nia M. Gomes
- 关键词：conservation laws ; discontinuous Galerkin ; implicit time integration ; upwind artificial diffusion ; adaptivity ; wavelets
- 刊名：Numerical Algorithms
- 出版时间：July 2005
- 出版年：2005
- 期刊代码：48_10171398
- 类别：mt
- 卷：39
- 期：1-3
- 页码：143-154
- 数据来源：sp
摘要
In this paper, space adaptivity is introduced to control the error in the numerical solution of hyperbolic systems of conservation laws. The reference numerical scheme is a new version of the discontinuous Galerkin method, which uses an implicit diffusive term in the direction of the streamlines, for stability purposes. The decision whether to refine or to unrefine the grid in a certain location is taken according to the magnitude of wavelet coefficients, which are indicators of local smoothness of the numerical solution. Numerical solutions of the nonlinear Euler equations illustrate the efficiency of the method.