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

Abstract

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.