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Mathematics of Computation

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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
MathSciNet review: 1325867
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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
Article copyright: © Copyright 1996 American Mathematical Society