On the Galerkin finite element approximations to multi-dimensional differential and integro-differential parabolic equations

DOI10.1007/BF02510212zbMath0876.65092OpenAlexW2143432837MaRDI QIDQ1359966

Nikolai Yu. Bakaev

Publication date: 24 August 1997

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02510212

zbMATH Keywords

integro-differential equationserror estimatesGalerkin finite element methodsemidiscretizationparabolic typeoperator method

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Integro-partial differential equations (45K05) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) 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) Initial value problems for second-order parabolic equations (35K15) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

Related Items (3)

Space-time spectral method for a weakly singular parabolic partial integro-differential equation on irregular domains ⋮ Fully spectral collocation method for nonlinear parabolic partial integro-differential equations ⋮ Error estimates and adaptive finite element methods

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Maximum-norm-stability and error-estimates in Galerkin methods for parabolic equations in one space variable
• The stability in L\(^q\) of the L\(^2\)-projection into finite element function spaces
• A remark on the \(L^{\infty}\) bounds of the Ritz operator associated with a finite element approximation
• L_∞-boundedness of the finite element galerkin operator for parabolic problems
• Ritz–Volterra Projections to Finite-Element Spaces and Applications to Integrodifferential and Related Equations
• Error Estimates for Spatially Discrete Approximations of Semilinear Parabolic Equations with Nonsmooth Initial Data
• Error Estimates for Semidiscrete Finite Element Methods for Parabolic Integro-Differential Equations
• Some Convergence Estimates for Semidiscrete Galerkin Type Approximations for Parabolic Equations
• On Fully Discrete Galerkin Approximations for Partial Integro-Differential Equations of Parabolic Type
• Resolvent Estimates for Elliptic Finite Element Operators in One Dimension
• Maximum Norm Analysis of Completely Discrete Finite Element Methods for Parabolic Problems

This page was built for publication: On the Galerkin finite element approximations to multi-dimensional differential and integro-differential parabolic equations