A continuous space-time finite element method for the wave equation
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- by Donald A. French and Todd E. Peterson PDF
- Math. Comp. 65 (1996), 491-506 Request permission
Abstract:
We consider a finite element method for the nonhomogeneous second-order wave equation, which is formulated in terms of continuous approximation functions in both space and time, thereby giving a unified treatment of the spatial and temporal discretizations. Our analysis uses primarily energy arguments, which are quite common for spatial discretizations but not for time.
We present a priori nodal (in time) superconvergence error estimates without any special time step restrictions. Our method is based on tensor-product spaces for the full discretization.
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Additional Information
- Donald A. French
- Affiliation: Department of Mathematical Sciences (ML 25), University of Cincinnati, Cincinnati, Ohio 45221
- Todd E. Peterson
- Affiliation: Department of Applied Mathematics, University of Virginia, Charlottesville, Virginia 22903
- Received by editor(s): August 3, 1994
- Received by editor(s) in revised form: March 6, 1995
- Additional Notes: Research of the first author was supported in part by the University of Cincinnati through the University Research Council and Taft Grants-in-aid as well as the Army Research Office by grant 28535-MA
- © Copyright 1996 American Mathematical Society
- Journal: Math. Comp. 65 (1996), 491-506
- MSC (1991): Primary 65M15
- DOI: https://doi.org/10.1090/S0025-5718-96-00685-0
- MathSciNet review: 1325867