First - Order System Least - Squares for Second - Order

The rst-order system least-squares methodology represents an alternative to standard mixed nite element methods. Among its advantages is the fact that the nite element spaces approximating the pressure and ux variables are not restricted by the inf-sup condition and that the least-squares functional itself serves as an appropiate error measure. This paper studies the rst-order system least-squares approach for scalar second-order elliptic boundary value problems with discontinuous coeecients. Elliptic-ity of an appropriately scaled least-squares bilinear form is shown independently of the size of the jumps in the coeecients leading to adequate nite element approximation results. The occurrence of singularities at interface corners and cross-points is discussed, and a weighted least-squares functional is introduced to handle such cases. Numerical experiments are presented for two test problems to illustrate the performance of this approach.