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- W2014915898 abstract "In plane domains with corners for the Bilaplacian a uniquely solvable conform variational principle is studied on weighted Sobolev spaces which is equivalent to the standard Dirichlet problem in the weak form. Clamped plates under point forces near corners are handled by this approach. With weighted Hsieh-Clough-Tocher elements on regular triangulations as conform C1-finite elements a new error analysis is performed without higher regularity assumptions on the exact solution than given by the data and the boundary. The rate of convergence of the error depends on the eigenvalue with smallest imaginary part of a clamped infinite wedge since this eigenvalue describes the singularity of the exact solution in a sector with same angle. Using different spaces of trial and test functions in the standard Galerkin procedure it is shown that the error in the weighted energy norm does not pollute. For convex corners asymptotic error estimates, are proved yielding convergence for a mixed method in hydrodynamics where the solution of a system of 2nd order and its Laplacian are approximated simultaneously by C0-finite elements being piecewise polynomials." @default.
- W2014915898 created "2016-06-24" @default.
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- W2014915898 date "1979-01-01" @default.
- W2014915898 modified "2023-09-27" @default.
- W2014915898 title "Conform and mixed finite element schemes for the Dirichlet problem for the Bilaplacian in plane domains with corners" @default.
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- W2014915898 doi "https://doi.org/10.1002/mma.1670010305" @default.
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