Maxwell算子的混合不连续Galerkin方法分析
Analysis of a hybridizable discontinuous Galerkin method for the Maxwell operator
中文总结 AI 辅助
本文研究了Maxwell算子的混合不连续Galerkin方法，通过不连续多项式近似获得数值解，基于混合curl-curl形式进行误差分析，证明了在高和低正则性情况下方法的稳定性和最优收敛性，并通过数值实验验证理论结果。
中文摘要 AI 辅助
在本文中，我们研究了Maxwell算子的混合不连续Galerkin（HDG）方法。唯一的全局未知数定义在元间边界上，数值解通过不连续多项式近似获得。误差分析基于Maxwell方程的混合curl-curl形式。在更一般正则性要求下获得了理论结果。特别是对于低正则性情况，对边界上的近似数据进行了特殊处理。证明了HDG方法在高和低正则性情况下都具有稳定性和最优收敛性。进行了包含光滑和奇异解析解的数值实验以验证理论结果。
英文摘要
In this paper, we study a hybridizable discontinuous Galerkin (HDG) method for the Maxwell operator. The only global unknowns are defined on the inter-element boundaries, and the numerical solutions are obtained by using discontinuous polynomial approximations. The error analysis is based on a mixed curl-curl formulation for the Maxwell equations. Theoretical results are obtained under a more general regularity requirement. In particular for the low regularity case, special treatment is applied to approximate data on the boundary. The HDG method is shown to be stable and convergence in an optimal order for both high and low regularity cases. Numerical experiments with both smooth and singular analytical solutions are performed to verify the theoretical results.
