An hp-local Discontinuous Galerkin Method for Parabolic Integro-Differential Equations
KAUST Grant NumberKUK-C1-013-04
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AbstractIn 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. © 2010 Springer Science+Business Media, LLC.
CitationPani AK, Yadav S (2010) An hp-local Discontinuous Galerkin Method for Parabolic Integro-Differential Equations. Journal of Scientific Computing 46: 71–99. Available: http://dx.doi.org/10.1007/s10915-010-9384-z.
SponsorsThe authors gratefully acknowledge the research support of the Department of Science and Technology, Government of India through project No. 08DST012. They also acknowledge Professor Neela Nataraj for her valuable suggestions and help on the numerical experiments. This publication is also based on work supported in part by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST). Further, the authors thank both the referees for their valuable comments and suggestions.
JournalJournal of Scientific Computing