Least-Squares Mixed Finite Elements for Second-Order Elliptic Problems
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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 O(h-2). Optimal error estimates are developed, especially in the case of differing polynomial degrees for the primary solution approximation uh and the flux approximation σh. Numerical experiments, confirming the theoretical rates of convergence, are presented.
author list (cited authors)
Pehlivanov, A. I., Carey, G. F., & Lazarov, R. D.