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• W2066500060 abstract "A fictitious domain method is presented for solving elliptic partial differential equations using Galerkin spectral approximation. The fictitious domain approach consists in immersing the original domain into a larger and geometrically simpler one in order to avoid the use of boundary fitted or unstructured meshes. In the present study, boundary constraints are enforced using Lagrange multipliers and the novel aspect is that the Lagrange multipliers are associated with smooth forcing functions, compactly supported inside the fictitious domain. This allows the accuracy of the spectral method to be preserved, unlike the classical discrete Lagrange multipliers method, in which the forcing is defined on the boundaries. In order to have a robust and efficient method, equations for the Lagrange multipliers are solved directly with an influence matrix technique. Using a Fourier–Chebyshev approximation, the high-order accuracy of the method is demonstrated on one- and two-dimensional elliptic problems of second- and fourth-order. The principle of the method is general and can be applied to solve elliptic problems using any high order variational approximation." @default.
• W2066500060 created "2016-06-24" @default.
• W2066500060 creator A5001435595 @default.
• W2066500060 creator A5079098906 @default.
• W2066500060 date "2011-04-01" @default.
• W2066500060 modified "2023-10-09" @default.
• W2066500060 title "A spectral fictitious domain method with internal forcing for solving elliptic PDEs" @default.
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• W2066500060 doi "https://doi.org/10.1016/j.jcp.2010.12.004" @default.
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