Finite Difference Schemes for Partial Differential Equations with Weak Solutions and Irregular Coefficients

DOI10.2478/CMAM-2004-0004zbMath1049.65112OpenAlexW2284085504MaRDI QIDQ4809786

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Publication date: 31 August 2004

Published in: Computational Methods in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2478/cmam-2004-0004

zbMATH Keywords

convergencenonlinear parabolic equationSobolev spaceweak solutionheat equationwave equationboundary value problemsfinite difference schemePoisson equationsingular coefficients

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Heat equation (35K05) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Wave equation (35L05) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) PDEs with low regular coefficients and/or low regular data (35R05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Finite difference methods for boundary value problems involving PDEs (65N06) Higher-order parabolic equations (35K25)

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Consistent convergence rate estimates in the grid \(W_{2,0}^2(\omega)\) norm for difference schemes approximating nonlinear elliptic equations with mixed derivatives and solutions from \(W_{2,0}^m(\Omega)\), \(3 < m \leq 4\) ⋮ Approximations to problems of optimal control of leading coefficients of elliptic equations in nondivergence form with an unbounded nonlinearity in the coefficients

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