On finite element schemes of the dirichlet problem
- 1 January 1981
- journal article
- research article
- Published by Taylor & Francis in Numerical Functional Analysis and Optimization
- Vol. 3 (1) , 105-136
- https://doi.org/10.1080/01630568108816081
Abstract
In this paper, we consider finite element schemes applied to the Dirichlet problem for the system of nonlinear elliptic equations, based on piecewise linear polynomials, and present iterative methods for solving algebraic nonlinear equations, which construct monotone sequences. Furthermore, we derive error estimates which imply uniform convergence. Our results are based on the discrete maximum principle. Finally, some typical numerical examples are given to demonstrate the usefulness of convergence results.Keywords
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