An hp-local Discontinuous Galerkin Method for Parabolic Integro-Differential Equations
DSpace at IIT Bombay
View Archive InfoField | Value | |
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
|
|