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Please use this identifier to cite or link to this item: http://dspace.library.iitb.ac.in/jspui/handle/100/13975

Title: An hp-local Discontinuous Galerkin Method for Parabolic Integro-Differential Equations
Authors: PANI, AK
YADAV, S
Keywords: FINITE-ELEMENT METHODS
DIFFERENTIAL-EQUATIONS
ELLIPTIC PROBLEMS
CONVECTION
DIFFUSION
APPROXIMATION
Issue Date: 2011
Publisher: SPRINGER/PLENUM PUBLISHERS
Citation: JOURNAL OF SCIENTIFIC COMPUTING,46(1)71-99
Abstract: 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.
URI: http://dx.doi.org/10.1007/s10915-010-9384-z
http://dspace.library.iitb.ac.in/jspui/handle/100/13975
ISSN: 0885-7474
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