| Title:
|
Space-time adaptive $hp$-FEM: Methodology overview (English) |
| Author:
|
Šolín, Pavel |
| Author:
|
Segeth, Karel |
| Author:
|
Doležel, Ivo |
| Language:
|
English |
| Journal:
|
Programs and Algorithms of Numerical Mathematics |
| Volume:
|
Proceedings of Seminar. Dolní Maxov, June 1-6, 2008 |
| Issue:
|
2008 |
| Year:
|
|
| Pages:
|
185-200 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We present a new class of self-adaptive higher-order finite element methods ($hp$-FEM) which are free of analytical
error estimates and thus work equally well for virtually all PDE problems ranging from simple linear elliptic equations to complex time-dependent nonlinear multiphysics coupled problems. The methods do not contain any tuning parameters and work reliably with both
low- and high-order finite elements. The methodology was used to solve various types of problems including thermoelasticity, microwave heating, flow of thermally conductive liquids etc. In this paper we use a combustion problem described by a system of two coupled nonlinear parabolic equations for illustration. The algorithms presented in this paper are available under the GPL
license in the form of a modular C++ library HERMES. () |
| MSC:
|
65M60 |
| idZBL:
|
Zbl 05802259 |
| . |
| Date available:
|
2015-09-08T11:37:26Z |
| Last updated:
|
2023-06-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/702873 |
| . |
