Order‐Optimal Preconditioners for Implicit Runge–Kutta Schemes Applied to Parabolic PDEs

DOI10.1137/05064093XzbMath1133.65071OpenAlexW1998953621MaRDI QIDQ5444257

Gunnar Andreas Staff, Kent-André Mardal, Trygve K. Nilssen

Publication date: 25 February 2008

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/05064093x

zbMATH Keywords

stabilityheat equationfinite element methodnumerical experimentsimplicit Euler methodsemidiscretizationpreconditionersRunge-Kutta schemesRunge-Kutta time discretizationparabolic PDECrank-Nicolson schemes

Mathematics Subject Classification ID

Heat equation (35K05) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Iterative numerical methods for linear systems (65F10) Numerical computation of matrix norms, conditioning, scaling (65F35) 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) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

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