Flux reconstruction for the \(P2\) nonconforming finite element method with application to a posteriori error estimation
Two \(H(\text{div},\Omega)\)-conforming flux reconstruction approaches for the \(P2\) nonconforming finite element method are presented. The reconstruction methods are introduced by considering a standard elliptic boundary value problem of second order. In the second part, the results are extended to the Stokes problem. Two different local (element-by-element) approaches are discussed, which lead to flux reconstructions in first-order Raviart-Thomas, respectively, Brezzi-Douglas-Marini spaces. Both alternatives are then applied to a posteriori error estimation. Some numerical experiments for the Poisson equation, respectively, the Stokes problem illustrate the performance of the newly introduced methods.
\(P2\) nonconforming finite element method
scientific article; zbMATH DE number 6104868
scientific article