Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations by Gabriel R. Barrenechea Franco Brezzi Andrea Cangiani & Emmanuil H. Georgoulis

Author:Gabriel R. Barrenechea, Franco Brezzi, Andrea Cangiani & Emmanuil H. Georgoulis
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

thus the VTCR solution is unique in the Trefftz space and coercivity in L 2(Ω) norm holds (the analogous result for C 1 = −C 2 = 1∕2 is proved in [70, Proposition 2]). However, this does not extend to the setting we considered so far, i.e. propagating waves with : in this case it can easily be shown that for all such that v = 0 on all elements adjacent to the Robin boundary Γ R and for any choice , thus well-posedness can not be ensured using a coercivity argument. Following [70, Proposition 2], for , we have:

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