Discrete Sobolev spaces and regularity of elliptic difference schemes

DOI10.1051/m2an/1991250506071zbMath0733.65058OpenAlexW2284829320MaRDI QIDQ3359678

Rob P. Stevenson

Publication date: 1991

Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/193642

zbMATH Keywords

minimal regularitydiscrete (fractional order) Sobolev spaceselliptic finite difference schemesregularity of elliptic difference schemes

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Finite difference methods for boundary value problems involving PDEs (65N06)

Related Items (6)

Uniform Error Estimates for Navier--Stokes Flow with an Exact Moving Boundary Using the Immersed Interface Method ⋮ Uniform \(W^{1,p}\) estimates and large-scale regularity for Dirichlet problems in perforated domains ⋮ Diffraction of waves on square lattice by semi-infinite rigid constraint ⋮ Growth of Sobolev norms and strong convergence for the discrete nonlinear Schrödinger equation ⋮ Continuum limit of discrete Sommerfeld problems on square lattice ⋮ Large-scale Lipschitz estimates for elliptic systems with periodic high-contrast coefficients

Cites Work

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• On the regularity of difference schemes. II: Regularity estimates for linear and nonlinear problems
• On the regularity of difference schemes
• Elliptische Differenzenoperatoren unter Dirichlet-Randbedingungen
• Elliptic difference equations and interior regularity
• Convergence of Multi-Grid Iterations Applied to Difference Equations
• Interior Regularity Estimates for Elliptic Systems of Difference Equations

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