0438628 - ÚT 2015 RIV US eng J - Článek v odborném periodiku
Šolín, Pavel - Korous, L.
Adaptive higher-order finite element methods for transient PDE problems based on embedded higher-order implicit Runge-Kutta methods.
Journal of Computational Physics. Roč. 231, č. 4 (2012), s. 1635-1649. ISSN 0021-9991. E-ISSN 1090-2716
Grant CEP: GA AV ČR IAA100760702
Výzkumný záměr: CEZ:AV0Z20760514
Klíčová slova: Runge-Kutta method * Butcher's table * finite element method
Kód oboru RIV: JA - Elektronika a optoelektronika, elektrotechnika
Impakt faktor: 2.138, rok: 2012

We present a new class of adaptivity algorithms for time-dependent partial differential equations (PDE) that combine adaptive higher-order finite elements (hp-FEM) in space with arbitrary (embedded, higher-order, implicit) Runge-Kutta methods in time. Weak formulation is only created for the stationary residual, and the Runge-Kutta methods are specified via their Butcher's tables. Around 30 Butcher's tables for various Runge-Kutta methods with numerically verified orders of local and global truncation errors are provided. A time-dependent benchmark problem with known exact solution that contains a sharp moving front is introduced, and it is used to compare the quality of seven embedded implicit higher-order Runge-Kutta methods. Numerical experiments also include a comparison of adaptive low-order FEM and hp-FEM with dynamically changing meshes. All numerical results presented in this paper were obtained using the open source library Hermes (http://www.hpfem.org/hermes) and they are reproducible in the Networked Computing Laboratory (NCLab) at http://www.nclab.com. (C) 2011 Elsevier Inc. All rights reserved.
Trvalý link: http://hdl.handle.net/11104/0242066