| Title:
|
Linear scheme for finite element solution of nonlinear parabolic-elliptic problems with nonhomogeneous Dirichlet boundary condition (English) |
| Author:
|
Říhová-Škabrahová, Dana |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
46 |
| Issue:
|
2 |
| Year:
|
2001 |
| Pages:
|
103-144 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The computation of nonlinear quasistationary two-dimensional magnetic fields leads to a nonlinear second order parabolic-elliptic initial-boundary value problem. Such a problem with a nonhomogeneous Dirichlet boundary condition on a part $\Gamma \!_1$ of the boundary is studied in this paper. The problem is discretized in space by the finite element method with linear functions on triangular elements and in time by the implicit-explicit method (the left-hand side by the implicit Euler method and the right-hand side by the explicit Euler method). The scheme we get is linear. The strong convergence of the method is proved under the assumptions that the boundary $\partial \Omega $ is piecewise of class $C^3$ and the initial condition belongs to $L_2$ only. Strong monotonicity and Lipschitz continuity of the form $a(v,w)$ is not an assumption, but a property of this form following from its physical background. (English) |
| Keyword:
|
finite element method |
| Keyword:
|
parabolic-elliptic problems |
| Keyword:
|
two-dimensional electromagnetic field |
| MSC:
|
35M10 |
| MSC:
|
65M12 |
| MSC:
|
65M60 |
| MSC:
|
65N30 |
| MSC:
|
78M10 |
| idZBL:
|
Zbl 1066.65117 |
| idMR:
|
MR1818081 |
| DOI:
|
10.1023/A:1013783722140 |
| . |
| Date available:
|
2009-09-22T18:06:07Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134460 |
| . |
| Reference:
|
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| Reference:
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| . |
