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Some further properties of the superconvergent flux projection. (English) Zbl 0996.65109

Summary: Some properties of the integral superconvergent flux (post-processing) projection formula are investigated: (1) A Green-Gauss formula together with the partition of unity property of the finite element basis imply global and local conservation properties and a local flux or stress recovery strategy; (2) The equivalence to a Lagrange multiplier mixed formulation is used to interpret the associated consistency requirement on the flux expansion via an inf-sup or LBB condition and (3) The resulting conditions on the flux basis are examined and the presence of oscillatory modes is demonstrated.

MSC:

65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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