Conditional space-time stability of collocation Runge-Kutta for parabolic evolution equations

zbMath1297.65104MaRDI QIDQ2510837

J. Schweitzer, Roman Andreev

Publication date: 4 August 2014

Published in: ETNA. Electronic Transactions on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: http://www.emis.de/journals/ETNA/volumes/2011-2020/vol41/abstract_vol41_pp62-80.html

zbMATH Keywords

numerical examplesPetrov-Galerkin methodparabolic evolution equationsspace-time variational formulationRunge-Kutta collocation methodspace-time stability

Mathematics Subject Classification ID

Abstract parabolic equations (35K90) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) 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) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

Related Items (7)

Wavelet-In-Time Multigrid-In-Space Preconditioning of Parabolic Evolution Equations ⋮ Stability and discretization error analysis for the Cahn–Hilliard system via relative energy estimates ⋮ A second-order fully-balanced structure-preserving variational discretization scheme for the Cahn–Hilliard–Navier–Stokes system ⋮ Preconditioning the Augmented Lagrangian Method for Instationary Mean Field Games with Diffusion ⋮ Numerical methods for the deterministic second moment equation of parabolic stochastic PDEs ⋮ Space-time discretization of the heat equation ⋮ The $L^2$-Projection and Quasi-Optimality of Galerkin Methods for Parabolic Equations

Uses Software

• RADAU
• na14
• OPQ

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