Least-Squares Mixed Finite Elements for Second-Order Elliptic Problems

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 $u_h $ and the flux approximation $\sigma _h $. Numerical experiments, confirming the theoretical rates of convergence, are presented.

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