Some New Mixed Element Schemes For Solving Mixed Second Order Elliptic Problem

In this paper, we present a new mixed variational form for second order elliptic problem. Based on the new form, we give some new solving schemes of any order which satisfy strongly elliptic condition and B-B condition. Theory analysis show that these schemes are of simpler and more convenient. Moreover, based on the so-called regularity assumption, we obtain optimal error estimates . Furthermore, under the maximal angle condition and coordinate system condition, we give the anisotrpic error estimates . Finally under the new form, we analyse several lower nonconforming solving schemes and give the anisotropic error estimates.