| Title:
|
Higher order finite element approximation of a quasilinear elliptic boundary value problem of a non-monotone type (English) |
| Author:
|
Liu, Liping |
| Author:
|
Křížek, Michal |
| Author:
|
Neittaanmäki, Pekka |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
41 |
| Issue:
|
6 |
| Year:
|
1996 |
| Pages:
|
467-478 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A nonlinear elliptic partial differential equation with homogeneous Dirichlet boundary conditions is examined. The problem describes for instance a stationary heat conduction in nonlinear inhomogeneous and anisotropic media. For finite elements of degree $k\ge 1$ we prove the optimal rates of convergence $\mathcal O(h^k)$ in the $H^1$-norm and $\mathcal O(h^{k+1})$ in the $L^2$-norm provided the true solution is sufficiently smooth. Considerations are restricted to domains with polyhedral boundaries. Numerical integration is not taken into account. (English) |
| Keyword:
|
nonlinear boundary value problem |
| Keyword:
|
finite elements |
| Keyword:
|
rate of convergence |
| Keyword:
|
anisotropic heat conduction |
| MSC:
|
35J65 |
| MSC:
|
65N30 |
| MSC:
|
74A15 |
| idZBL:
|
Zbl 0870.65096 |
| idMR:
|
MR1415252 |
| DOI:
|
10.21136/AM.1996.134338 |
| . |
| Date available:
|
2009-09-22T17:52:57Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134338 |
| . |
| Reference:
|
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