An <Emphasis Type="Italic">hp</Emphasis>-local Discontinuous Galerkin Method for Parabolic Integro-Differential Equations |
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Authors: | Amiya K Pani Sangita Yadav |
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Affiliation: | (1) School of Mathematics, University of Minnesota, 127 Vincent Hall, 206 Church St SE, Minneapolis, MN 55455, USA |
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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. |
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Keywords: | |
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