Thursday, November 16, 2023 - 15:40 in V2-210/216
A pollution-free ultra-weak FOSLS discretization of the Helmholtz equation
A talk in the BI.discrete Workshop series by
Harald Monsuur from Amsterdam
| Abstract: |
We consider an ultra-weak first order system discretization of the Helmholtz equation.
When employing the optimal test norm, the `ideal' method yields the best approximation to the pair of the Helmholtz solution and its scaled gradient w.r.t. the norm on $L_2(\Omega)\times L_2(\Omega)^d$ from the selected finite element trial space.
On convex polygons, the `practical', implementable method is shown to be pollution-free essentially whenever the order $\tilde{p}$ of the finite element test space grows proportionally with $\max(\log \kappa,p^2)$, with $p$ being the order at trial side.
Recently, we have investigated the possibilities of preconditioning the resulting saddle-point system. We give satisfying numerical results on convex polygons.
Within the CRC this talk is associated to the project(s): A7, B3, B7 |
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