Galerkin and Runge-Kutta methods: unified formulation, a posteriori error estimates and nodal superconvergence

DOI10.1007/s00211-011-0363-6zbMath1228.65125OpenAlexW1988040707MaRDI QIDQ634613

Ricardo H. Nochetto, Georgios D. Akrivis, Charalambos G. Makridakis

Publication date: 16 August 2011

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00211-011-0363-6

zbMATH Keywords

Hilbert spacesemidiscretizationRunge-Kutta methodsa posteriori error estimateslinear differential equationGalerkin methodstime discretization of parabolic equations

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) 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) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Error bounds for numerical methods for ordinary differential equations (65L70) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Linear differential equations in abstract spaces (34G10) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50) Numerical solutions to abstract evolution equations (65J08)

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Uses Software

• RODAS

Cites Work

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