SUPERCONVERGENCE OF LEAST-SQUARES MIXED FINITE ELEMENT FOR SECOND-ORDER ELLIPTIC PROBLEMS

• 来源期刊: 计算数学（英文版）
• 关键词: Elliptic problem Superconvergence Interpolation projection Least-squares mixed finite element.
• 年，卷（期）: 2003,（6）
• 页码范围: 825-832
• 页数: 8页
• 语种: 英文

摘要

In this paper the least-squares mixed finite element is considered for solving secondorder 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 Hi-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-DouglasFortin-Marini elements of order r are employed with optimal error estimate of O(hr+1).