A pollution-free ultra-weak FOSLS discretization of the Helmholtz equation

03/29/2023

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by   Harald Monsuur, et al.

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We consider an ultra-weak first order system discretization of the Helmholtz equation. By 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(Ω)× L_2(Ω)^d from the selected finite element trial space. On convex polygons, the `practical', implementable method is shown to be pollution-free when the polynomial degree of the finite element test space grows proportionally with logκ. Numerical results also on other domains show a much better accuracy than for the Galerkin method.