Abstract
A family of bicubic Hermite elements is considered which involves a rectangular element and two triangular ones including a triangular element with a curved side. The triangular elements are used in combination with the rectangular ones only near the boundary of a domain and provide interelement continuity of an approximate solution. Special attention is paid to the triangular element with a curved side since it is nonconforming in the sense of the Dirichlet boundary condition. For the Poisson equation the convergence estimate in the energy norm is proved.
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Submitted by A. V. Lapin
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Gileva, L., Shaydurov, V. Bicubic Hermite Elements in a Domain with the Curved Boundary. Lobachevskii J Math 39, 893–903 (2018). https://doi.org/10.1134/S1995080218070119
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DOI: https://doi.org/10.1134/S1995080218070119