EXPANDED MIXED FINITE-ELEMENT METHODS FOR LINEAR 2ND-ORDER ELLIPTIC PROBLEMS

We develop a new mixed formulation for the numerical solution of secon d-order elliptic problems. This new formulation expands the standard m ixed formulation in the sense that three variables are explicitly trea ted: the scalar unknown, its gradient, and its pur (the coefficient ti mes the gradient). Based on this formulation, mixed finite element app roximations of the second-order elliptic problems are considered. Opti mal order error estimates in the L-P- and H- (S)-norms are obtained fo r the mixed approximations. Various implementation techniques for solv ing the systems of algebraic equations are discussed. A postprocessing method for improving the scalar variable is analyzed and superconverg ent estimates in the L-P-norm are derived. The mixed formulation is su itable for the case where the coefficient of differential equations is a small tensor and does not need to be inverted. (C) Elsevier, Paris.