SIAM Journal on Numerical Analysis
Finite element methods with numerical quadrature for parabolic integrodifferential equations
SIAM Journal on Numerical Analysis
The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
SIAM Journal on Numerical Analysis
An A Priori Error Analysis of the Local Discontinuous Galerkin Method for Elliptic Problems
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
An hp-Analysis of the Local Discontinuous Galerkin Method for Diffusion Problems
Journal of Scientific Computing
Local discontinuous Galerkin methods for nonlinear dispersive equations
Journal of Computational Physics
Galerkin Finite Element Methods for Parabolic Problems (Springer Series in Computational Mathematics)
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In this article, a priori error bounds are derived for an hp-local discontinuous Galerkin (LDG) approximation to a parabolic integro-differential equation. It is shown that error estimates in L 2-norm of the gradient as well as of the potential are optimal in the discretizing parameter h and suboptimal in the degree of polynomial p. Due to the presence of the integral term, an introduction of an expanded mixed type Ritz-Volterra projection helps us to achieve optimal estimates. Further, it is observed that a negative norm estimate of the gradient plays a crucial role in our convergence analysis. As in the elliptic case, similar results on order of convergence are established for the semidiscrete method after suitably modifying the numerical fluxes. The optimality of these theoretical results is tested in a series of numerical experiments on two dimensional domains.