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 |
| State | Published - Nov 12 1997 |
| Externally published | Yes |
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Keywords
- BDM space
- Minimal surfaces
- Mixed method
- Nonlinear elliptic problem
ASJC Scopus subject areas
- Applied Mathematics
- Computational Mathematics
- Numerical Analysis
Cite this
Mixed finite element methods for nonlinear elliptic problems : The h-p version. / Lee, Miyoung; Milner, Fabio.
In: Journal of Computational and Applied Mathematics, Vol. 85, No. 2, 12.11.1997, p. 239-261.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Mixed finite element methods for nonlinear elliptic problems
T2 - The h-p version
AU - Lee, Miyoung
AU - Milner, Fabio
PY - 1997/11/12
Y1 - 1997/11/12
N2 - 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.
AB - 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.
KW - BDM space
KW - Minimal surfaces
KW - Mixed method
KW - Nonlinear elliptic problem
UR - http://www.scopus.com/inward/record.url?scp=0031274106&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0031274106&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:0031274106
VL - 85
SP - 239
EP - 261
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
SN - 0377-0427
IS - 2
ER -