关于Maxwell方程混合元方法的超收敛

Superconvergence of Mixed Methods for the Maxwell's Equations

本文讨论Ｍａｘｗｅｌｌ方程的三种混合元方法（ＥＣＨＬ元，ＭＥＣＨＬ元，Ｎｅｄｅｌｅｃ’ｓ元）在一般（非均匀）矩形网格上的超收敛性。研究结果表明，ＭＥＸＨＬ元和Ｎｅｄｅｌｅｃ’ｓ元在非均匀网格上具有超收敛性，而ＥＣＨＬ元只在均匀网格上才有超收敛。此外，本文还证明ＥＣＨＬ元在非均匀矩形网格上也有Ｏ（ｈ）的收敛阶，这是以前一直没有解决的问题。在本文中采用正是我们小组惯用的积分恒等式工具，问题的解决也表明了这一工具的通用性。

In this paper,the superconvergence of three mixed methods (ECHL,MECHL,Nedelec's)for Maxwell's equations are discused on the nonuniform rectangular meshes.It is proved that there is superconvergence on the nonuniform rectangular meshes for MECHL element and Nedelec's element.But for ECHL element,there is superconv.ergence only on the uniform recangular meshes.And the convergence of O(h)for ECHL element on the nonuniform meshes is proved which has been a open problem.