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An hp-local Discontinuous Galerkin Method for Parabolic Integro-Differential Equations

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Title An hp-local Discontinuous Galerkin Method for Parabolic Integro-Differential Equations
 
Creator PANI, AK
YADAV, S
 
Subject FINITE-ELEMENT METHODS
DIFFERENTIAL-EQUATIONS
ELLIPTIC PROBLEMS
CONVECTION
DIFFUSION
APPROXIMATION
LDG method
Parabolic integro-differential equation
Semidiscrete
Mixed type Ritz-Volterra projection
Negative norm estimates
Role of stabilizing parameters
Optimal error bounds
 
Description 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.
 
Publisher SPRINGER/PLENUM PUBLISHERS
 
Date 2012-06-26T05:31:25Z
2012-06-26T05:31:25Z
2011
 
Type Article
 
Identifier JOURNAL OF SCIENTIFIC COMPUTING,46(1)71-99
0885-7474
http://dx.doi.org/10.1007/s10915-010-9384-z
http://dspace.library.iitb.ac.in/jspui/handle/100/13975
 
Language English