Adaptive multilevel finite element approximations of semilinear elliptic boundary value problems |
| |
Authors: | Mats G Larson A Jonas Niklasson |
| |
Institution: | Department of Mathematics, Chalmers University of Technology, S-412 96 G?teborg, Sweden; e-mail: mgl@math.chalmers.se, SE Division of Mechanics, Chalmers University of Technology, S-412 96 G?teborg, Sweden; e-mail: jnik@mec.chalmers.se, SE
|
| |
Abstract: | Summary. In this paper we consider two aspects of the problem of designing efficient numerical methods for the approximation of semilinear
boundary value problems. First we consider the use of two and multilevel algorithms for approximating the discrete solution.
Secondly we consider adaptive mesh refinement based on feedback information from coarse level approximations. The algorithms
are based on an a posteriori error estimate, where the error is estimated in terms of computable quantities only. The a posteriori
error estimate is used for choosing appropriate spaces in the multilevel algorithms, mesh refinements, as a stopping criterion
and finally it gives an estimate of the total error.
Received April 8, 1997 / Revised version received July 27, 1998 / Published online September 24, 1999 |
| |
Keywords: | Mathematics Subject Classification (1991):65N30 65N12 65N15 65N50 65N55 |
本文献已被 SpringerLink 等数据库收录! |
|