Bridging the hybrid high-order and hybridizable discontinuous Galerkin methods 论文
2015ESAIM Mathematical Modelling and Numerical Analysis引用 218
Advanced Numerical Methods in Computational MathematicsDifferential Equations and Numerical MethodsAdvanced Mathematical Modeling in Engineering
详细信息
- 发表期刊/会议
- ESAIM Mathematical Modelling and Numerical Analysis
- 发表日期
- 2015-07-17
- 发表年份
- 2015
关键词
Advanced Numerical Methods in Computational MathematicsDifferential Equations and Numerical MethodsAdvanced Mathematical Modeling in Engineering
摘要
We build a bridge between the hybrid high-order (HHO) and the hybridizable discontinuous Galerkin (HDG) methods in the setting of a model diffusion problem. First, we briefly recall the construction of HHO methods and derive some new variants. Then, by casting the HHO method in mixed form, we identify the numerical flux so that the HHO method can be compared to HDG methods. In turn, the incorporation of the HHO method into the HDG framework brings up new, efficient choices of the local spaces and a new, subtle construction of the numerical flux ensuring optimal orders of convergence on meshes made of general shape-regular polyhedral elements. Numerical experiments comparing two of these methods are shown.