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• W2277309680 abstract "We develop a discontinuous cut finite element method for the Laplace–Beltrami operator on a hypersurface embedded in |$mathbb {R}^d$|⁠. The method is constructed by using a discontinuous piecewise linear finite element space defined on a background mesh in |$mathbb {R}^d$|⁠. The surface is approximated by a continuous piecewise linear surface that cuts through the background mesh in an arbitrary fashion. Then, a discontinuous Galerkin method is formulated on the discrete surface and in order to obtain coercivity, certain stabilization terms are added on the faces between neighbouring elements that provide control of the discontinuity as well as the jump in the gradient. We derive optimal a priori error and condition number estimates which are independent of the positioning of the surface in the background mesh. Finally, we present numerical examples confirming our theoretical results." @default.
• W2277309680 created "2016-06-24" @default.
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• W2277309680 date "2016-03-04" @default.
• W2277309680 modified "2023-09-30" @default.
• W2277309680 title "A cut discontinuous Galerkin method for the Laplace–Beltrami operator" @default.
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• W2277309680 doi "https://doi.org/10.1093/imanum/drv068" @default.
• W2277309680 hasPublicationYear "2016" @default.
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