Ημερομηνία : Δευτέρα 4 Μαΐου , 2026

Ώρα : 12:50

Τοποθεσία : Αίθουσα Σεμιναρίων του Τομέα Μαθηματικών ΣΕΜΦΕ, κτ. Ε΄, 2ος όροφος

Ομιλητής: κ. Brian Hennessy (Heriot-Watt University)

Τίτλος Ομιλίας : Space-time finite element methods for nonlinear wave equations via elliptic regularisation

Περίληψη : In this talk we present algorithms for solving nonlinear wave equations (NLW) based on an elliptic regularisation approach conjectured by Ennio De Giorgi. This approach guarantees existence and uniqueness to a solution of a regularised nonlinear wave equation which is elliptic and converges to a solution of NLW, even in cases where the NLW is not well posed.

Using this framework, we propose a conforming finite element method for solving the NLW via space-time finite elements which inherits desirable properties of the continuous problem with particular attention being paid to the time discretisation and stability of the algorithm.

We will also examine a Discontinuous Galerkin approach via a symmetric interior penalty(SIP) method, which also inherits well posedness from the continuous problem and allows for the scheme to be reformulated as a multiscale time-stepping algorithm.

This talk is based on joint work with Lehel Banjai (Heriot-Watt University) & Emmanuil Georgoulis (NTUA & Heriot-Watt University &  FORTH).