Element Methods For Integro-differential Equations Research Articles

A Hybrid Stress Finite Element Method for Integro-Differential Equations Modelling Dynamic Fractional Order Viscoelasticity

A Hybrid Stress Finite Element Method for Integro-Differential Equations Modelling Dynamic Fractional Order Viscoelasticity

Mixed virtual element method for integro-differential equations of parabolic type

Mixed virtual element method for integro-differential equations of parabolic type

Richardson extrapolation and defect correction of mixed finite element methods for integro-differential equations in porous media

Asymptotic error expansions in the sense of L ∞-norm for the Raviart-Thomas mixed finite element approximation by the lowest-order rectangular element associated with a class of parabolic integro-differential equations on a rectangular domain are derived, such that the Richardson extrapolation of two different schemes and an interpolation defect correction can be applied to increase the accuracy of the approximations for both the vector field and the scalar field by the aid of an interpolation postprocessing technique, and the key point in deriving them is the establishment of the error estimates for the mixed regularized Green’s functions with memory terms presented in R. Ewing at al., Int. J. Numer. Anal. Model 2 (2005), 301–328. As a result of all these higher order numerical approximations, they can be used to generate a posteriori error estimators for this mixed finite element approximation.

Error estimates for semidiscrete Galerkin approximation to a time dependent parabolic integro-differential equation with nonsmooth data

In this paper, an attempt has been made to carry over known results for the finite element Galerkin method for a time dependent parabolic equation with nonsmooth initial data to an integro-differential equation of parabolic type. More precisely, for the homogeneous problem a standard energy technique in conjunction with a duality argument is used to obtain an L2-error estimate of order \(\) for the semidiscrete solution when the given initial function is only in L2. Further, for the nonhomogeneous case with zero initial condition, an error estimate of order \(\) uniformly in time is proved, provided that the nonhomogeneous term is in L∞(L2). The present paper provides a complete answer to an open problem posed on p. 106 of the book Finite Element Methods for Integro-differential Equations by Chen and Shih.