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Least-squares mixed finite elements for second-order elliptic problems. (English) Zbl 0806.65108

Authors’ summary: A theoretical analysis of a least squares mixed finite element method for second-order elliptic problems in two- and three- dimensional domains is presented. It is proved that the method is not subject to the LBB condition, and that the finite element approximation yields a symmetric positive definite linear system with condition number \({\mathcal O}(h^{-2})\). Optimal error estimates are developed, especially in the case of differing polynomial degrees for the primary solution approximation \(u_ h\) and the flux approximation \(\sigma_ h\). Numerical experiments, confirming the theoretical rates of convergence, are presented.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
65F10 Iterative numerical methods for linear systems
65F35 Numerical computation of matrix norms, conditioning, scaling
35J25 Boundary value problems for second-order elliptic equations
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