In this paper we propose two stabilized finite element methods for different functional frameworks of the wave equation in mixed form. These stabilized finite element methods are stable for any pair of interpolation spaces of the unknowns. The variational forms corresponding to different functional settings are treated in a unified manner through the introduction of length scales related to the unknowns. Stability and convergence analysis is performed together with numerical experiments. It is shown that modifying the length scales allows one to mimic at the discrete level the different functional settings of the continuous problem and influence the stability and accuracy of the resulting methods.

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Published on 05/09/19

DOI: 10.1137/130918708
Licence: CC BY-NC-SA license

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