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• W2022694169 abstract "We study the numerical solution of a class of parabolic integro-differential equations with weakly singular kernels. We use an $hp$-version discontinuous Galerkin (DG) method for the discretization in time. We derive optimal $hp$-version error estimates and show that exponential rates of convergence can be achieved for solutions with singular (temporal) behavior near $t=0$ caused by the weakly singular kernel. Moreover, we prove that by using nonuniformly refined time steps, optimal algebraic convergence rates can be achieved for the h-version DG method. We then combine the DG time-stepping method with a standard finite element discretization in space, and present an optimal error analysis of the resulting fully discrete scheme. Our theoretical results are numerically validated in a series of test problems." @default.
• W2022694169 created "2016-06-24" @default.
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• W2022694169 date "2011-01-01" @default.
• W2022694169 modified "2023-09-25" @default.
• W2022694169 title "An $hp$-Version Discontinuous Galerkin Method for Integro-Differential Equations of Parabolic Type" @default.
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• W2022694169 doi "https://doi.org/10.1137/100797114" @default.
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