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• W2897058341 abstract "We consider solving the surface Helmholtz equation on a smooth two dimensional surface embedded into a three dimensional space meshed with tetrahedra. The mesh does not respect the surface and thus the surface cuts through the elements. We consider a Galerkin method based on using the restrictions of continuous piecewise linears defined on the tetrahedra to the surface as trial and test functions.Using a stabilized method combining Galerkin least squares stabilization and a penalty on the gradient jumps we obtain stability of the discrete formulation under the condition $h k < C$, where $h$ denotes the mesh size, $k$ the wave number and $C$ a constant depending mainly on the surface curvature $kappa$, but not on the surface/mesh intersection. Optimal error estimates in the $H^1$ and $L^2$-norms follow." @default.
• W2897058341 created "2018-10-26" @default.
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• W2897058341 date "2018-10-09" @default.
• W2897058341 modified "2023-09-27" @default.
• W2897058341 title "A Stable Cut Finite Element Method for Partial Differential Equations on Surfaces: The Helmholtz-Beltrami Operator" @default.
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• W2897058341 hasPublicationYear "2018" @default.
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