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An h-p Petrov-Galerkin finite element method for linear Volterra integro-differential equations |
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| Authors: | LiJun Yi BenQi Guo |
| Institution: | 1. Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China 2. Division of Computational Science, E-institute of Shanghai Universities, Shanghai, 200234, China 3. Department of Mathematics, University of Manitoba, Winnipeg, MB, R3T 2N2, Canada |
| Abstract: | We analyze an h-p version Petrov-Galerkin finite element method for linear Volterra integrodifferential equations. We prove optimal a priori error bounds in the L 2- and H 1-norm that are explicit in the time steps, the approximation orders and in the regularity of the exact solution. Numerical experiments confirm the theoretical results. Moreover, we observe that the numerical scheme superconverges at the nodal points of the time partition. |
| Keywords: | Volterra integro-differential equations h-p finite element method Petrov-Galerkin method timestepping scheme |
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