DSpace at IIT Bombay >
IITB Publications >
Please use this identifier to cite or link to this item:
|Title: ||An hp-local Discontinuous Galerkin Method for Parabolic Integro-Differential Equations|
|Authors: ||PANI, AK|
|Keywords: ||FINITE-ELEMENT METHODS|
|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.|
|Appears in Collections:||Article|
Files in This Item:
There are no files associated with this item.
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.