A continuous space-time finite element method

for the wave equation

Authors:
Donald A. French and Todd E. Peterson

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

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Abstract | References | Similar Articles | Additional Information

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

DOI:
https://doi.org/10.1090/S0025-5718-96-00685-0

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

Article copyright:
© Copyright 1996
American Mathematical Society