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	A unifying theory of a posteriori error control for nonconforming finite element methods
	Carstensen, C. ; Hu, Jun
	2007
关键词	DISCONTINUOUS GALERKIN METHODS 2ND-ORDER ELLIPTIC PROBLEMS PLANAR LINEAR ELASTICITY NAVIER-STOKES EQUATIONS INCOMPRESSIBLE ELASTICITY MIXED FEM APPROXIMATIONS CONVERGENCE ESTIMATORS
英文摘要	Residual-based a posteriori error estimates were derived within one unifying framework for lowest-order conforming, nonconforming, and mixed finite element schemes in Carstensen [Numer Math 100: 617-637, 2005]. Therein, the key assumption is that the conforming first-order finite element space V(h)(c) annulates the linear and bounded residual l written V(h)(c)subset of ker l. That excludes particular nonconforming finite element methods (NCFEMs) on parallelograms in that V(h)(c) not subset of ker l. The present paper generalises the aforementioned theory to more general situations to deduce new a posteriori error estimates, also for mortar and discontinuous Galerkin methods. The key assumption is the existence of some bounded linear operator Pi : V(h)(c) -> V(h)(nc) with some elementary properties. It is conjectured that the more general hypothesis (H1)-(H3) can be established for all known NCFEMs. Applications on various nonstandard finite element schemes for the Laplace, Stokes, and Navier-Lame equations illustrate the presented unifying theory of a posteriori error control for NCFEM.; Mathematics, Applied; SCI(E); 0; ARTICLE; 3; 473-502; 107
语种	英语
出处	SCI
出版者	numerische mathematik
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/249794]
专题	数学科学学院
推荐引用方式 GB/T 7714	Carstensen, C.,Hu, Jun. A unifying theory of a posteriori error control for nonconforming finite element methods. 2007-01-01.

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