Semidiscrete Finite Element Methods for Linear and Semilinear Parabolic Problems with Smooth Interfaces: Some New Optimal Error Estimates

DOI10.1080/01630563.2011.651189zbMath1250.65112OpenAlexW2064751445MaRDI QIDQ2895677

Tazuddin Ahmed, Bhupen Deka

Publication date: 4 July 2012

Published in: Numerical Functional Analysis and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/01630563.2011.651189

zbMATH Keywords

finite element methodsemidiscretizationoptimal error estimateslinear parabolic interface problemsemilinear parabolic interface problems

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Semilinear parabolic equations (35K58)

Related Items (7)

A partially penalty immersed Crouzeix-Raviart finite element method for interface problems ⋮ Local discontinuous Galerkin methods for parabolic interface problems with homogeneous and non-homogeneous jump conditions ⋮ Analysis of a Fully Discrete Finite Element Method for Parabolic Interface Problems with Nonsmooth Initial Data ⋮ \textit{A priori} \(L^{\infty}(L^2)\) error estimates for finite element approximations to parabolic integro-differential equations with discontinuous coefficients ⋮ Unnamed Item ⋮ Linearized four-step implicit scheme for nonlinear parabolic interface problems ⋮ Approximation of linear hyperbolic interface problems on finite element: some new estimates

Cites Work

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• Galerkin finite element methods for parabolic problems
• A priori error estimates in the finite element method for nonself-adjoint elliptic and parabolic interface problems
• Finite element methods with numerical quadrature for elliptic problems with smooth interfaces
• Finite element methods for semilinear elliptic and parabolic interface problems
• Finite dimensional approximation of nonlinear problems. I: Branches of nonsingular solutions
• Finite element methods and their convergence for elliptic and parabolic interface problems
• Finite Element Methods for Navier-Stokes Equations
• On the Smoothing Property of the Galerkin Method for Parabolic Equations
• Optimal Error Estimates for Linear Parabolic Problems with Discontinuous Coefficients

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