非自伴椭圆问题的离散强极值原理与区域分解法

1．引言本文考虑非自伴二阶椭圆型方程的边值问题（）：其中Q是有界多角形开域，其边界＊O充分光滑；并且方程左端微分算子是H’川椭圆的．虽然在一定条件下问题（P）的解满足极值原理，但是，用通常的Galerkin有限元法求解（P）时，得到的解叫的一般并不满足极值原理．特别，当问＞＞a时，qx）还可能出现剧烈的振荡．即使对自伴问题（即（卫．1）中b一时在三角形线性元的情形，P．G．O。小t和P．－A．Ravlart证明了：如果限定三角形的内角。三。／2－。（其中常数。＞则，且网格参数人＞0充分小时，则有较弱形式的极值原理：maxfrU（…

STRONGLY DISCRETE MAXIMUM PRINCIPLE AND DOMAIN DECOMPOSITION METHOD FOR NON-SELF-ADJOINT ELLIPTIC PROBLEM

The solution of the boundary-vaue problem for non-self-adjoint elliptic equa tions is approximated by Partial Upwind Finite Element method, where all the angles of the triangles a are /2 but the mesh parameter h are arbitrary and which insures the validity of the strongly maximum principle for the discrete prob-lem. The Schwarz alternating method will enable us to break the discrete linear system into several linear subsystems of smaller size and we shall show that the approximate solutions from Schwarz domain decomposition method converge to the exact solution of the linear system geometrically and uniformly.