Optimal error estimates of two mixed finite element methods for parabolic integro-differential equations with nonsmooth initial data

DOI10.1007/s10915-012-9666-8zbMath1275.65093OpenAlexW2025417229MaRDI QIDQ1955943

Sangita Yadav, Deepjyoti Goswami, Amiya K. Pani

Publication date: 19 June 2013

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-012-9666-8

zbMATH Keywords

convergencesuperconvergenceoptimal error estimatessemidiscrete Galerkin approximationparabolic integro-differential equationnonsmooth initial dataCauchy-Dirichlet mixed problemRitz-Volterra projectionstwo mixed finite element methods

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Integro-partial differential equations (45K05) Linear integral equations (45A05)

Related Items

Expanded mixed FEM with lowest order RT elements for nonlinear and nonlocal parabolic problems, Superconvergence analysis for nonlinear parabolic equation with \(EQ_1^{\mathrm{rot}}\) nonconforming finite element, Mixed FEM for time-fractional diffusion problems with time-dependent coefficients, HDG method for linear parabolic integro-differential equations, Parallel two-grid finite element method for the time-dependent natural convection problem with non-smooth initial data, Optimal error estimates of mixed FEMs for second order hyperbolic integro-differential equations with minimal smoothness on initial data, The Weak Galerkin Finite Element Method for Solving the Time-Dependent Integro-Differential Equations, Unconditional superconvergence analysis for nonlinear parabolic equation with \(EQ_1^{rot}\) nonconforming finite element, A fully discrete two-grid finite element method for nonlinear hyperbolic integro-differential equation, A priori error estimates of expanded mixed FEM for Kirchhoff type parabolic equation, Finite element methods: research in India over the last decade

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Numerical methods for hyperbolic and parabolic integro-differential equations
• Non-classical \(H^ 1\) projection and Galerkin methods for non-linear parabolic integro-differential equations
• Error estimates for semidiscrete Galerkin approximation to a time dependent parabolic integro-differential equation with nonsmooth data
• Finite volume element approximations of nonlocal in time one-dimensional flows in porous media
• Mixed Finite Element Approximations of Parabolic Integro-Differential Equations with Nonsmooth Initial Data
• An Alternate Approach to OptimalL²-Error Analysis of Semidiscrete Galerkin Methods for Linear Parabolic Problems with Nonsmooth Initial Data
• Ritz–Volterra Projections to Finite-Element Spaces and Applications to Integrodifferential and Related Equations
• Error Estimates for Semidiscrete Finite Element Methods for Parabolic Integro-Differential Equations
• L^∞(L²)andL^∞(L^∞)error estimates for mixed methods for integro-differential equations of parabolic type
• Mixed and Hybrid Finite Element Methods
• Expanded mixed finite element methods for linear second-order elliptic problems, I
• Expanded mixed finite element methods for quasilinear second order elliptic problems, II
• Mixed Finite Elements for Elliptic Problems with Tensor Coefficients as Cell-Centered Finite Differences
• SharpL²-Error Estimates and Superconvergence of Mixed Finite Element Methods for Non-Fickian Flows in Porous Media
• Finite Element Methods with Numerical Quadrature for Parabolic Integrodifferential Equations
• Analysis of Expanded Mixed Finite Element Methods for a Nonlinear Parabolic Equation Modeling Flow into Variably Saturated Porous Media
• Finite volume element approximations of nonlocal reactive flows in porous media
• Some new error estimates of a semidiscrete finite volume element method for a parabolic integro-differential equation with nonsmooth initial data