Abstract
Mixed finite element methods for strongly nonlinear second order elliptic problems are proposed and analyzed. Existence and uniqueness of the approximate solution are demonstrated using a fixed point argument. Convergence and stability of the method are proved both with respect to mesh refinement and increase of the degree of the approximating polynomials. The analysis is carried out in detail using Raviart-Thomas-Nedelec spaces as an example. Numerical results for minimal surface problems are obtained using Brezzi-Douglas-Marini spaces. Graphs of the approximate solutions are presented for two different problems.
Original language | English (US) |
---|---|
Pages (from-to) | 239-261 |
Number of pages | 23 |
Journal | Journal of Computational and Applied Mathematics |
Volume | 85 |
Issue number | 2 |
DOIs | |
State | Published - Nov 12 1997 |
Externally published | Yes |
Keywords
- BDM space
- Minimal surfaces
- Mixed method
- Nonlinear elliptic problem
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics