Some Improvements Of Wilson's Element By Combined Hybrid Finite Element Methods With Const Stress Mode

The combined hybrid method is of an intrinsic of enhancing coarse-mesh-accuracyand stability of lower order displacement schemes. it satisfying the so-called inf-subcondition or LBB stabilize condition is not necessary, so it's ?exible to select the stressmode, the patch const stress mode can work well. The combination parameter playsan important role in adjusting the energy error without refined meshes. Such kind ofimprovement can be realized without more computational cost, since the stress param-eters can be eliminated at the element level.This paper is devoted to improvement ofthe nonconforming Wilson's element by the combined hybrid method with the mostsimplest stress mode–the constant mode: the improvement without modified noncon-forming strain terms,the improvement with modified nonconforming strain terms Nu-merical experiments show that the improved version can attain a higher numericalaccuracy than that of Wilson's element, and the second method can avoid the poisson-locking. Numerical experiments show that the improved version can attain a highernumerical accuracy than that of Wilson's element. the energy compatibility condition,introduced in Zhou (Combined hybrid finite element method without requirement forBabuska-Brezzi condition, to appear) is the ultimate key to the achievement of highperformance.