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.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received April 8, 1997 / Revised version received July 27, 1998 / Published online September 24, 1999
Rights and permissions
About this article
Cite this article
Larson, M., Niklasson, A. Adaptive multilevel finite element approximations of semilinear elliptic boundary value problems. Numer. Math. 84, 249–274 (1999). https://doi.org/10.1007/s002110050471
Issue Date:
DOI: https://doi.org/10.1007/s002110050471