Superconvergence of least-squares mixed finite element for symmetric elliptic problems

Authors:
Yanping Chen;Manping Zhang
Affiliations:
Department of Mathematics, Xiangtan University, Hunan, People's Republic of China;Department of Mathematics, Fudan University, Shanghai, People's Republic of China
Venue:
Applied Numerical Mathematics
Year:
2004

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Abstract

We formulate a least-squares mixed finite element method over quadrilaterals. The superconvergence result obtaineded between the finite element approximation and our appropriate-chosen interpolation of the exact solution 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). Numerical results are included.