International Journal for Numerical Methods in Engineering · 1980 · 71 citations · 5 references
ComputingComputational EngineeringComputational MechanicsFinite Element AnalysisFinite Element MethodsBoundary Element MethodsConvergence AnalysisFinite Element DiscretizationFinite Element FormulationNumerical AlgorithmsBoundary ProblemBoundary Value Problem SolversFinite Element ModelingNonconforming Finite ElementsPiecewise Continuous FunctionsPiecewise Functions
Abstract A simple approximation by nonconforming finite elements is presented that passes the patch test of Irons and Strang but does not yield approximate solutions converging to the solution of the given boundary value problem. It is constructed from continuous piecewise linear functions perturbed by step functions. Further, strange convergence properties of such approximations are explained in all details because they may be typical for the behaviour of nonconforming finite elements violating the basic precondition for convergence.
5
Stéphane Crépey, Olivier Guéant, David Hobson et al. · HAL (Le Centre pour la Communication Scientifique Directe) · 2011 · 10.2K citations
An Analysis of the Finite Element Method
E. I., Gilbert Strang, George J. Fix · Mathematics of Computation · 1974 · 3.5K citations
Computing, Computational Engineering, Mechanical Engineering +12