Adaptive higher-order finite element methods for transient PDE problems based on embedded higher-order implicit Runge-Kutta methods

DOI10.1016/j.jcp.2011.10.023zbMath1242.65204OpenAlexW2116457998MaRDI QIDQ422983

Lukas Korous, Pavel Šolín

Publication date: 18 May 2012

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2011.10.023

zbMATH Keywords

finite element methodnumerical experimentserror boundsRunge-Kutta methodsemidiscretizationautomatic adaptivityButcher's tabledynamically changing meshesreproducible research

Mathematics Subject Classification ID

Nonlinear first-order PDEs (35F20) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

Related Items (3)

On the accuracy, stability and computational efficiency of explicit last-stage diagonally implicit Runge-Kutta methods (ELDIRK) for the adaptive solution of phase-field problems ⋮ Nonlinear higher-order transient solver for magnetic fluid hyperthermia ⋮ Hermes2D, a C++ library for rapid development of adaptive \(hp\)-FEM and \(hp\)-DG solvers

Uses Software

• TR-BDF2

Cites Work

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• Discontinuoushp-Finite Element Methods for Advection-Diffusion-Reaction Problems
• Adaptive Space‐Time Finite Element Methods for Parabolic Optimization Problems
• Computing with hp-ADAPTIVE FINITE ELEMENTS

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