Erath, C., Mascotto, L., Melenk, J. M., Perugia, I., & Rieder, A. (2022). Mortar Coupling of 𝘩𝘱-Discontinuous Galerkin and Boundary Element Methods for the Helmholtz Equation. Journal of Scientific Computing, 92(1), Article 2. https://doi.org/10.1007/s10915-022-01849-0
We design and analyze a coupling of a discontinuous Galerkin finite element method with a boundary element method to solve the Helmholtz equation with variable coefficients in three dimensions. The coupling is realized with a mortar variable that is related to an impedance trace on a smooth interface. The method obtained has a block structure with nonsingular subblocks. We prove quasi-optimality of the 𝘩- and 𝘱-versions of the scheme, under a threshold condition on the approximability properties of the discrete spaces. Amongst others, an essential tool in the analysis is a novel discontinuous-to-continuous reconstruction operator on tetrahedral meshes with curved faces.
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Project title:
Numerische Methoden Höherer Ordnung für nichtlokale Operatoren: F 6507-N36 (Fonds zur Förderung der wissenschaftlichen Forschung (FWF))
