Error analysis of splitting methods for inhomogeneous evolution equations

DOI10.1016/j.apnum.2012.06.002zbMath1267.65085OpenAlexW2058247185MaRDI QIDQ450906

Alexander Ostermann, Katharina Schratz

Publication date: 26 September 2012

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

Full work available at URL: https://doi.org/10.1016/j.apnum.2012.06.002

zbMATH Keywords

Banach spacesnumerical resultsevolution equationstrongly continuous semigroupssplitting methodsparabolic problemsLie-splitting trapezoidal splittingmaximal dissipative operators

Mathematics Subject Classification ID

Abstract parabolic equations (35K90) Nonlinear differential equations in abstract spaces (34G20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Error bounds for numerical methods for ordinary differential equations (65L70)

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Error analysis of a fully discrete discontinuous Galerkin alternating direction implicit discretization of a class of linear wave-type problems ⋮ The error structure of the Douglas-Rachford splitting method for stiff linear problems ⋮ Compatibility conditions for Dirichlet and Neumann problems of Poisson's equation on a rectangle ⋮ Stability and convergence of product formulas for operator matrices ⋮ The analysis of operator splitting methods for the Camassa-Holm equation ⋮ Error analysis of an ADI splitting scheme for the inhomogeneous Maxwell equations ⋮ A splitting/polynomial chaos expansion approach for stochastic evolution equations

Cites Work

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• Semigroups of linear operators and applications to partial differential equations
• Error bounds for exponential operator splittings
• Dimension splitting for time dependent operators
• Dimension splitting for evolution equations
• Splitting methods
• Geometric Numerical Integration
• Analytic semigroups and optimal regularity in parabolic problems

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