In this paper the least-squares mixed finite element is considered for solving second-order elliptic problems in two dimensional domains. The primary solution u and the flux σ are approximated using finite element sp...In this paper the least-squares mixed finite element is considered for solving second-order elliptic problems in two dimensional domains. The primary solution u and the flux σ are approximated using finite element spaces consisting of piecewise polynomials of degree k and r respectively. Based on interpolation operators and an auxiliary projection, superconvergent H1-error estimates of both the primary solution approximation uh and the flux approximation σh are obtained under the standard quasi-uniform assumption on finite element partition. The superconvergence indicates an accuracy of O(hr+2) for the least-squares mixed finite element approximation if Raviart-Thomas or Brezzi-Douglas-Fortin-Marini elements of order r are employed with optimal error estimate of O(hr+1).展开更多
基金Supported by National Science Foundation of China and the Foundation of China State Education Commission and the Special Funds for Major State Basic Research Projects.
文摘In this paper the least-squares mixed finite element is considered for solving second-order elliptic problems in two dimensional domains. The primary solution u and the flux σ are approximated using finite element spaces consisting of piecewise polynomials of degree k and r respectively. Based on interpolation operators and an auxiliary projection, superconvergent H1-error estimates of both the primary solution approximation uh and the flux approximation σh are obtained under the standard quasi-uniform assumption on finite element partition. The superconvergence indicates an accuracy of O(hr+2) for the least-squares mixed finite element approximation if Raviart-Thomas or Brezzi-Douglas-Fortin-Marini elements of order r are employed with optimal error estimate of O(hr+1).
