thursday 25 Maggio 2017Dalle 14:00A posteriori error analysis and adaptive schemes for the wave equationMOX Seminar Series

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Event Details

Aposteriori error estimates provide a rigorous foundation for the derivation of efficient adaptive
algorithms for the approximation of solutions of partial differential equations (PDEs). While the
literature is rich with results for the approximation of elliptic and parabolic PDEs, it is much less
developed for the hyperbolic equations such as the acoustic or elastic wave equations. In this
talk, I will review some of the “standard” aposteriori results for the scalar linear wave equation,
including those of [1] and [2], and present recent improvements and further developments to
lower order Sobolev norms based on Baker’s Trick [3] for backward Euler schemes.
Subsequent focus will be given to practically relevant methods such as Verlet, Cosine, or
Newmark methods, a popular example of which is the Leap-frog method [4].
Notes: This is based on joint work with E.H. Georgoulis, C. Makridakis and J.M. Virtanen.
References:
[1] W. Bangerth and R. Rannacher, J. Comput. Acoust. 9(2):575–591, 2001.
[2] C. Bernardi and E. Süli, Math. Models Methods Appl. Sci. 15(2):199–225, 2005.
[3] E. H. Georgoulis, O. Lakkis, and C. Makridakis. IMA J. Numer. Anal., 33(4):1245–1264,
2013, http://arxiv.org/abs/1003.3641
[4] E. H. Georgoulis, O. Lakkis, C. Makridakis, and J. M. Virtanen. SIAM J. Numer. Anal.,

Date e orari

giovedì 25 Maggio 2017
Dalle 14:00

Luogo

Politecnico di Milano, Aula Seminari 'Saleri'

Via Bonardi, 9 - Milano

Organizzatore

Politecnico di Milano

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