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...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Journal |
| Published: |
2018
|
| Subjects: | |
| Online Access: | https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84929903856&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/54661 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| 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. |
|---|