ESAIM Mathematical Modelling and Numerical Analysis · 2015 · 295 citations · 33 references
ComputingComputational EngineeringComputational MechanicsFinite Element AnalysisFinite Element MethodsConvergence AnalysisError EstimationFinite Difference MethodsFinite Element DiscretizationFinite Element FormulationElliptic Boundary-value ProblemsError Estimation For Finite Element SolutionsFinite Difference DiscretizationNonconforming Finite Elements
We introduce the nonconforming Virtual Element Method (VEM) for the approximation of second order elliptic problems. We present the construction of the new element in two and three dimensions, highlighting the main differences with the conforming VEM and the classical nonconforming finite element methods. We provide the error analysis and establish the equivalence with a family of mimetic finite difference methods. Numerical experiments verify the theory and validate the performance of the proposed method.
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