On the regularity of difference schemes

DOI10.1007/BF02384470zbMath0462.65058OpenAlexW2061993727MaRDI QIDQ1152937

Wolfgang Hackbusch

Publication date: 1981

Published in: Arkiv för Matematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02384470

zbMATH Keywords

convergenceSobolev spaceoptimal error estimateselliptic difference schemesLipschitz regionsmulti-grid iterationsstability of difference operators

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Difference operators (39A70) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)

Related Items (13)

Maximum Norm Regularity of Periodic Elliptic Difference Operators With Variable Coefficients ⋮ Estimates for the Green's function of the discrete Bilaplacian in dimensions 2 and 3 ⋮ On first and second order box schemes ⋮ Near-Tip Field for Diffraction on Square Lattice by Crack ⋮ Uniform Error Estimates for Navier--Stokes Flow with an Exact Moving Boundary Using the Immersed Interface Method ⋮ Diffraction of waves on square lattice by semi-infinite rigid constraint ⋮ The Dean-Kawasaki equation and the structure of density fluctuations in systems of diffusing particles ⋮ Local-basis difference potentials method for elliptic PDEs in complex geometry ⋮ Discrete Sommerfeld diffraction problems on hexagonal lattice with a zigzag semi-infinite crack and rigid constraint ⋮ Continuum limit of discrete Sommerfeld problems on square lattice ⋮ On the convergence of multi-grid methods with transforming smoothers ⋮ Discrete Sobolev spaces and regularity of elliptic difference schemes ⋮ Optimal-Order Finite Difference Approximation of Generalized Solutions to the Biharmonic Equation in a Cube

Cites Work

• On the multi-grid method applied to difference equations
• The Peaceman-Rachford method for small mesh increments
• Elliptische Differenzenoperatoren unter Dirichlet-Randbedingungen
• Elliptic difference equations and interior regularity
• Convergence of Multi-Grid Iterations Applied to Difference Equations
• Discrete Interior Schauder Estimates for Elliptic Difference Operators
• Convergence Estimates for Essentially Positive Type Discrete Dirichlet Problems
• Interior Estimates in $l^p $ for Elliptic Difference Operators
• The Numerical Solution of Laplace's Equation
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