High-order linearly implicit two-step peer - finite element methods for time-dependent PDEs

DOI10.1016/j.apnum.2008.03.017zbMath1160.65332OpenAlexW2000002033MaRDI QIDQ1007384

Helmut Podhaisky, Rüdiger Weiner, Alf Gerisch, Jens Lang

Publication date: 20 March 2009

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2008.03.017

zbMATH Keywords

numerical examplesmethod of linesfinite element softwareRothe methodRosenbrock methodtwo-step methodKARDOSpeer methodtime-dependent PDE

Mathematics Subject Classification ID

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) Initial value problems for second-order parabolic equations (35K15) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Packaged methods for numerical algorithms (65Y15)

Related Items (19)

IMEX peer methods for fast-wave-slow-wave problems ⋮ High-order linearly implicit two-step peer schemes for the discontinuous Galerkin solution of the incompressible Navier-Stokes equations ⋮ Discrete adjoint implicit peer methods in optimal control ⋮ Two-step peer methods with continuous output ⋮ Efficient A-stable peer two-step methods ⋮ Space-time adaptive linearly implicit peer methods for parabolic problems ⋮ A class of implicit peer methods for stiff systems ⋮ Robustness and efficiency of an implicit time-adaptive discontinuous Galerkin solver for unsteady flows ⋮ Exponentially fitted two-step peer methods for oscillatory problems ⋮ On the implementation of explicit two-step peer methods with Runge-Kutta stability ⋮ Extrapolation-based implicit-explicit Peer methods with optimised stability regions ⋮ Extrapolation-based super-convergent implicit-explicit peer methods with A-stable implicit part ⋮ Linearly implicit peer methods for the compressible Euler equations ⋮ Peer methods for the one-dimensional shallow-water equations with CWENO space discretization ⋮ Two-derivative Runge-Kutta methods for PDEs using a novel discretization approach ⋮ Superconvergent IMEX peer methods ⋮ A comparison of AMF- and Krylov-methods in Matlab for large stiff ODE systems ⋮ Partially implicit peer methods for the compressible Euler equations ⋮ Rosenbrock-Wanner Methods: Construction and Mission

Uses Software

• ROS3P
• RODAS
• KARDOS

Cites Work

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• Parallel `peer' two-step W-methods and their application to MOL-systems.
• Adaptive multilevel solution of nonlinear parabolic PDE systems. Theory, algorithm, and applications
• Rosenbrock-type `peer' two-step methods
• Two-dimensional cascadic finite element computations of combustion problems
• Multi-implicit peer two-step W-methods for parallel time integration
• Parallel Two-Step W-Methods with Peer Variables
• Runge-Kutta Approximation of Quasi-Linear Parabolic Equations
• Linearly implicit time discretization of non-linear parabolic equations
• Two-dimensional adaptive simulation of dopant diffusion in silicon
• ROS3P -- An accurate third-order Rosenbrock solver designed for parabolic problems

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