Convergence of a finite difference method for solving 2D parabolic interface problems

DOI10.1016/j.cam.2011.04.042zbMath1245.65117OpenAlexW2033374591MaRDI QIDQ432784

J. Herrera, H. S. Yoon

Publication date: 4 July 2012

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

Full work available at URL: https://doi.org/10.1016/j.cam.2011.04.042

zbMATH Keywords

convergenceerror boundsdifference schemeSobolev normabstract Carchy problemtwo-dimensional parabplic interface problems

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) 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) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Linear differential equations in abstract spaces (34G10)

Related Items (4)

Fractional order convergence rate estimate of finite-difference method for the heat equation with concentrated capacity ⋮ Finite difference approximation for the 2D heat equation with concentrated capacity ⋮ \textit{A priori} \(L^{\infty}(L^2)\) error estimates for finite element approximations to parabolic integro-differential equations with discontinuous coefficients ⋮ Numerical approximation of a two-dimensional parabolic time-dependent problem containing a delta function

Cites Work

• Convergence of finite difference method for the parabolic problem with concentrated capacity and variable operator
• Finite difference approximations for some interface problems with variable coefficients
• An introduction to partial differential equations
• Bounds for a class of linear functionals with applications to Hermite interpolation
• On the convergence of finite difference schemes for the heat equation with concentrated capacity
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