The Mathematical Institute, University of Oxford, Eprints Archive

An hp-Local Discontinuous Galerkin method for Parabolic
Integro-Differential Equations

Pani, A. K. and Yadav, S (2009) An hp-Local Discontinuous Galerkin method for Parabolic
Integro-Differential Equations.
Not specified . (Submitted)

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Abstract

In this article, a priori error analysis is discussed for an hp-local discontinuous Galerkin (LDG) approximation to a parabolic integro-differential equation. It is shown that the L2 -norm of the gradient and the L2 -norm 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 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.

Item Type:Article
Subjects:D - G > General
H - N > Numerical analysis
Research Groups:Oxford Centre for Collaborative Applied Mathematics
ID Code:840
Deposited By:Dr M. Stoll
Deposited On:16 Oct 2009 07:39
Last Modified:16 Oct 2009 07:39

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