Rajen Kumar Sinha

Optimal Error Estimates for Linear Parabolic Problems with Discontinuous Coefficients

A finite element discretization is proposed and analyzed for a linear parabolic problems with discontinuous coefficients. Due to low global regularity of the solution, it seems difficult to achieve optimal order of convergence with classical finite element methods [Numer. Math., 79 (1998), pp. 175--202]. In this paper, we have used a finite element discretization, where interface triangles are assumed to be curved triangles instead of straight triangles as in classical finite element methods. Optimal order error estimates in L2 and H1 norms are shown to hold even if the regularity of the solution is low on the whole domain. While the continuous time Galerkin method is discussed for the spatially discrete scheme, the discontinuous Galerkin method is analyzed for the fully discrete scheme. The interfaces and boundaries of the domains are assumed to be smooth for our purpose.

Some new error estimates of a semidiscrete finite volume element method for a parabolic integro-differential equation with nonsmooth initial data

A semidiscrete finite volume element (FVE) approximation to a parabolic integro-differential equation (PIDE) is analyzed in a two-dimensional convex polygonal domain. An optimal-order

Mixed Finite Element Approximations of Parabolic Integro-Differential Equations with Nonsmooth Initial Data

L^2

On the Convergence of Finite Element Method for Second Order Elliptic Interface Problems

-error estimate for smooth initial data and nearly the same optimal-order

Superconvergence of H 1-Galerkin mixed finite element methods for parabolic problems

L^2

Superconvergence of H 1-Galerkin Mixed Finite Element Methods for Second-Order Elliptic Equations

-error estimate for nonsmooth initial data are obtained. More precisely, for homogeneous equations, an elementary energy technique and a duality argument are used to derive an error estimate of order

L@ (L2) and L@ (H1) Norms Error Estimates in Finite Element Method for Linear Parabolic Interface Problems

O\left(t^{-1}{h^2}\ln h\right)

A posteriori error estimates for H 1-Galerkin mixed finite-element method for parabolic problems

in the

Finite element methods for second order linear hyperbolic interface problems

L^2

A posteriori error analysis of the Crank–Nicolson finite element method for linear parabolic interface problems: A reconstruction approach

-norm for positive time when the given initial function is only in