A class of discontinuous Petrov-Galerkin methods. Part III: Adaptivity

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• 作者：Leszek Demkowicz^a ; ^{leszek@ices.utexas.edu} ; Jay Gopalakrishnan^b ; ^jayg@ufl.edu ; Antti H. Niemi^a ; ^{ahniemi@ices.utexas.edu}
• 关键词：Convection-dominated diffusion ; hp-Adaptivity ; Discontinuous Petrov&ndash ; Galerkin
• 刊名：Applied Numerical Mathematics
• 出版年：2012
• 期刊代码：8_01689274
• 类别：cp
• 出版时间：April, 2012
• 卷：62
• 期：4
• 页码：396-427
• 文件大小：2923 K

摘要

We continue our theoretical and numerical study on the Discontinuous Petrov-Galerkin method with optimal test functions in context of 1D and 2D convection-dominated diffusion problems and hp-adaptivity. With a proper choice of the norm for the test space, we prove robustness (uniform stability with respect to the diffusion parameter) and mesh-independence of the energy norm of the FE error for the 1D problem. With hp-adaptivity and a proper scaling of the norms for the test functions, we establish new limits for solving convection-dominated diffusion problems numerically: for 1D and for 2D problems. The adaptive process is fully automatic and starts with a mesh consisting of few elements only.