求解二维时谐Maxwell方程的一种混合有限元新格式

A NEW MIXED FINITE ELEMENT SCHEME FOR SOLVING 2D TIME-HARMONIC MAXWELL-TYPE PROBLEM

本文,我们提出一种新的求解二维时谐Maxwell方程的H^1-协调节点连续混合有限元格式.由于加上若干稳定化项和投影项,得到的混合变分形式是稳定的.我们证明了双线性形式满足连续性,K_h-强制性和Inf-Sup条件,因此,解是存在唯一的.此外,我们也给出了拟优的误差估计和相应的收敛阶.

In this paper, we propose a new H^1-conforming nodal-continuous mixed finite element scheme. Several stabilizations and projections are added into the mixed finite element scheme and thus the stability of the variational system is achieved. We prove that the bilinear forms satisfy continuity, Kh-coercivity and Inf-Sup condition, and hence the existence and uniqueness of solution hold. Furthermore, quasi-optimal error estimates and convergence rate are derived.