Numerical results for an unconditionally stable spacetime finite element method for the wave equation
Abstract
In this work, we introduce a new spacetime variational formulation of the secondorder wave equation, where integration by parts is also applied with respect to the time variable, and a modified Hilbert transformation is used. For this resulting variational setting, ansatz and test spaces are equal. Thus, conforming finite element discretizations lead to GalerkinBubnov schemes. We consider a conforming tensorproduct approach with piecewise polynomial, continuous basis functions, which results in an unconditionally stable method, i.e., no CFL condition is required. We give numerical examples for a one and a twodimensional spatial domain, where the unconditional stability and optimal convergence rates in spacetime norms are illustrated.
 Publication:

arXiv eprints
 Pub Date:
 March 2021
 arXiv:
 arXiv:2103.04324
 Bibcode:
 2021arXiv210304324L
 Keywords:

 Mathematics  Numerical Analysis;
 65M12;
 65M60
 EPrint:
 9 pages