Abstract
Rothe’s method for time discretization and Crouseix-Raviart nonconforming finite element method to the spatial variable. After introducing error estimators, we prove the equivalence between the error and its indicators.
Highlights
1 Introduction Among commonly used methods for the numerical approach of problems which arise in engineering, for example, Laplace equation and Maxwell system, the finite element method is one of the most relied on methods because it is much more interested in the analysis of the error committed between the exact solution and the approximate solution
There are a lot of works on the a posteriori estimators for the elliptic partial differential equations and dynamic partial differential equations
It is possible to refer to [ ] where the authors considered an elliptic second order boundary value problem approximated by a discontinuous Galerkin method
Summary
Among commonly used methods for the numerical approach of problems which arise in engineering, for example, Laplace equation and Maxwell system, the finite element method is one of the most relied on methods because it is much more interested in the analysis of the error committed between the exact solution and the approximate solution. 3 Full discretization We consider the following nonconforming finite element method to approximate our problem. Let ζjihnt be the set of interior edges/faces of Υjh and ζT be the set of edges/faces of the element For any T ∈ Υjh, let wT be the union of all elements having a common edge/face with T.
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