TY - JOUR
T1 - The Defect Iteration of the Finite Element for Elliptic Boundary Value Problems and Petrov-Galerkin Approximation
AU - Gao , Junbin
AU - Yang , Yidu
AU - Shih , T. M.
JO - Journal of Computational Mathematics
VL - 2
SP - 152
EP - 164
PY - 1998
DA - 1998/04
SN - 16
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/9149.html
KW - Petrov-Galerkin approximation, defect iteration correction, interpolation operator.
AB - <p style="text-align: justify;">In this paper we introduce a Petrov-Galerkin approximation model to the solution of linear and semi-linear elliptic boundary value problems in which piecewise quadratic polynomial space and piecewise linear polynomial space are used as the shape function space and the test function space, respectively. We prove that the approximation order of the standard quadratic finite element can be attained in this Petrov-Galerkin model. Based on the so-called &quot;contractivity&quot; of the interpolation operator, we further prove that the defect iterative sequence of the linear finite element solution converge to the proposed Petrov-Galerkin approximate solution.</p>