A continuous space-time finite element method for the wave equation

French, Donald; Peterson, Todd

doi:10.1090/S0025-5718-96-00685-0

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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