An auxiliary equation method for obtaining superconvergent finite-element approximations

✍ Scribed by Johnson, Richard W. ;MacKinnon, Robert J.

• Publisher: Wiley (John Wiley & Sons)
• Year: 1992
• Tongue: English
• Weight: 405 KB
• Volume: 8
• Category: Article
• ISSN: 0748-8025
• DOI: 10.1002/cnm.1630080205

✦ Synopsis

A finite-element method is developed which improves accuracy and yields superconvergent approximations to two-dimensional elliptic boundary-value problems on a union of square bilinear elements. This method employs an auxiliary equation which is derived using a Taylor series analysis on the discrete formula obtained from a Galerkin finite-element formulation. Application of the finiteelement method to the auxiliary equation results in O(h4) convergence for problems with constant coefficients and improved accuracy for problems with variable coefficients. Supporting numerical examples are given. O ( h 2 ) truncation terms. 2 -5 The present study represents an extension of such methods to the finite-element method to obtain improved accuracy and high-order convergence. The present 2-D results extend to one and three dimensions.