An Alternate Approach to OptimalL2-Error Analysis of Semidiscrete Galerkin Methods for Linear Parabolic Problems with Nonsmooth Initial Data

DOI10.1080/01630563.2011.587334zbMath1243.65111OpenAlexW2112966273MaRDI QIDQ3173513

Deepjyoti Goswami, Amiya K. Pani

Publication date: 10 October 2011

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

Full work available at URL: https://doi.org/10.1080/01630563.2011.587334

zbMATH Keywords

Galerkin methodfinite element methodssuperconvergencemixed finite elementssemidiscretizationenergy argumentsoptimal error estimatesnonsmooth initial datamaximum norm estimatelinear parabolic initial boundary-value problem

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) 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) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

Related Items

Semidiscrete Finite Element Analysis of Time Fractional Parabolic Problems: A Unified Approach ⋮ Mixed FEM for time-fractional diffusion problems with time-dependent coefficients ⋮ Parallel two-grid finite element method for the time-dependent natural convection problem with non-smooth initial data ⋮ Optimal error estimates of two mixed finite element methods for parabolic integro-differential equations with nonsmooth initial data ⋮ OPTIMAL ESTIMATES FOR THE SEMIDISCRETE GALERKIN METHOD APPLIED TO PARABOLIC INTEGRO-DIFFERENTIAL EQUATIONS WITH NONSMOOTH DATA

Cites Work

• Optimal \(L_{\infty}\)-estimates for a mixed finite element method for second order elliptic and parabolic problems
• Quadrature based finite element approximations to time dependent parabolic equations with nonsmooth initial data
• Superconvergence of mixed finite element methods for parabolic problems with nonsmooth initial data
• Error estimates for semidiscrete Galerkin approximation to a time dependent parabolic integro-differential equation with nonsmooth data
• Mixed Finite Element Approximations of Parabolic Integro-Differential Equations with Nonsmooth Initial Data
• Error Estimates for Semidiscrete Finite Element Methods for Parabolic Integro-Differential Equations
• On the Smoothing Property of the Galerkin Method for Parabolic Equations
• Some Convergence Estimates for Semidiscrete Galerkin Type Approximations for Parabolic Equations
• Galerkin Finite Element Methods for Parabolic Problems

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