SUPERCONVERGENCE FOR ELLIPTIC PROBLEMS BY LEAST-SQUARES MIXED FINITE ELEMENT

摘要

In this paper the least-squares mixed finite element is considered for solving second-order elliptic problems. Based on projection operators and an auxiliary projection, superconvergent estimates of both the primary solution approximation u_h and the flux approximation σ_h are obtained. The superconvergence indicates an accuracy of O(h~(r+2)) for the least-squares mixed finite element approximation if Raviart-Thomas or Brezzi-Douglas-Fortin-Marini elements of order r are employed.