| Title:
|
Finite element solution of a hyperbolic-parabolic problem (English) |
| Author:
|
Hlavička, Rudolf |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
39 |
| Issue:
|
3 |
| Year:
|
1994 |
| Pages:
|
215-239 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Existence and finite element approximation of a hyperbolic-parabolic problem is studied. The original two-dimensional domain is approximated by a polygonal one (external approximations). The time discretization is obtained using Euler’s backward formula (Rothe’s method). Under certain smoothing assumptions on the data (see (2.6), (2.7)) the existence and uniqueness of the solution and the convergence of Rothe’s functions in the space $C(\overline{I},V)$ is proved. (English) |
| Keyword:
|
Rothe's method |
| Keyword:
|
finite elements. |
| Keyword:
|
Euler’s backward formula |
| Keyword:
|
linear parabolic or hyperbolic equations |
| Keyword:
|
convergence |
| MSC:
|
65M12 |
| MSC:
|
65M20 |
| MSC:
|
65M60 |
| MSC:
|
65N30 |
| idZBL:
|
Zbl 0812.65087 |
| idMR:
|
MR1273634 |
| DOI:
|
10.21136/AM.1994.134254 |
| . |
| Date available:
|
2009-09-22T17:43:56Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134254 |
| . |
| Reference:
|
[1] Demerdash, N.A., Gillot, D.H.: A new approach for determination of eddy current and flux penetration in nonlinear ferromagnetic materials.IEEE Trans. MAG-10 (1974), 682–685. |
| Reference:
|
[2] Gajewski, H., Gröger, K., Zacharias, K.: Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen.Akademie, Berlin, 1974. MR 0636412 |
| Reference:
|
[3] Hannalla, A.Y., Macdonald, D.C.: Numerical analysis of transient field problems in electrical machines.Proc. IEE 123 (1976), 893–898. |
| Reference:
|
[4] Kačur, J.: Method of Rothe in Evolution Equations.Teubner-Texte zur Mathematik, Band 80, Leipzig, 1985. MR 0834176 |
| Reference:
|
[5] Lütke-Daldrup, B.: Numerische Lösung zweidimensionaler nichtlinearer instantionärer Feld- und Wirbelstromprobleme.Archiv für Elektrotechnik 68 (1985), 223–228. 10.1007/BF01575911 |
| Reference:
|
[6] Melkes, F., Zlámal M.: Numerical solution of nonlinear quasistationary magnetic fields.Internat. J. Numer. Methods Engineering 19 (1983), 1053–1062. 10.1002/nme.1620190709 |
| Reference:
|
[7] Zlámal, M.: Curved elements in the finite element method.I. SIAM J. Numer. Anal. 10 (1973), 229–240. MR 0395263, 10.1137/0710022 |
| Reference:
|
[8] Zlámal, M.: Finite element solution of quasistationary nonlinear magnetic field.RAIRO Anal. Numér. 16 (1982), 161–191. MR 0661454, 10.1051/m2an/1982160201611 |
| Reference:
|
[9] Ženíšek A.: Finite element variational crimes in parabolic-elliptic problems.Numer. Math. 55 (1989), 343–376. MR 0993476, 10.1007/BF01390058 |
| Reference:
|
[10] Ženíšek, A.: Nonlinear Elliptic and Evolution Problems and Their Finite Element Approximations.Academic Press, London, 1990. MR 1086876 |
| . |
