摘要
本文讨论了非线性对流扩散方程的hp-局部间断Galerkin有限元方法,得到了关于网格尺寸h是最优以及关于逼近次数p是次优的hp-误差估计.本文给出了数值算例,数值结果表明,LDG方法比SIPG或NIPG方法更精确且LDG方法对于罚值不敏感,而SIPG及NIPG方法对于罚值敏感.
We consider the hp-local discontinuous Galerkin finite element methods for nonlinear con- vection diffusion problems and use the novel method to deal with the nonlinear convection term. We obtain the hp-error estimates that are optimal in the mesh-size h and slightly suboptimal in the approximation degree. A numerical example is presented in the paper. The numerical results demonstrate that the LDG method is more accurate than the SIPG method （or NIPG method） and the LDG method is not sensitive to the penalty value α for large ps, but the SIPG method and the NIPG method are sensitive to the penalty value for large ps.
出处
《工程数学学报》
CSCD
北大核心
2012年第6期894-906,共13页
Chinese Journal of Engineering Mathematics
