A priori error estimates for finite volume element approximations to second order linear hyperbolic integro-differential equations
© 2015 Institute for Scientific Computing and Information. In this paper, both semidiscrete and completely discrete finite volume element methods (FVEMs) are analyzed for approximating solutions of a class of linear hyperbolic integro-differential equations in a two-dimensional convex polygonal doma...
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| Main Authors: | , |
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| Format: | Journal |
| Published: |
2018
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| Subjects: | |
| Online Access: | https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84929903856&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/44750 |
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| Institution: | Chiang Mai University |
| Summary: | © 2015 Institute for Scientific Computing and Information. In this paper, both semidiscrete and completely discrete finite volume element methods (FVEMs) are analyzed for approximating solutions of a class of linear hyperbolic integro-differential equations in a two-dimensional convex polygonal domain. The effect of numerical quadrature is also examined. In the semidiscrete case, optimal error estimates in L < sup > ∞ < /sup > (L < sup > 2 < /sup > ) and L < sup > ∞ < /sup > (H < sup > 1 < /sup > ) norms are shown to hold with minimal regularity assumptions on the initial data, whereas quasi-optimal estimate is derived in L < sup > ∞ < /sup > (L < sup > ∞ < /sup > ) norm under higher regularity on the data. Based on a second order explicit method in time, a completely discrete scheme is examined and optimal error estimates are established with a mild condition on the space and time discretizing parameters. Finally, some numerical experiments are conducted which confirm the theoretical order of convergence. |
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