Least-squares mixed finite element methods for non-selfadjoint elliptic problems .1. Error estimates

A least-squares mixed finite element method for general second-order non-selfadjoint elliptic problems in two- and three-dimensional domains is formulated and analyzed. The finite element spaces for the primary solution approximation u(h) and the flux approximation sigma(h) consist of piecewise polynomials of degree k and r respectively. The method is mildly nonconforming on the boundary. The cases k = r and k + 1 = r are studied, It is proved that the method is not subject to the LBB-condition. Optimal L(2)- and H-1-error estimates are derived for regular finite element partitions. Numerical experiments, confirming the theoretical rates of convergence, are presented.