On Exact Results in the Finite Element Method |
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Authors: | Ivan Hlavacek Michal Krizek |
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Institution: | (1) Mathematical Institute, Academy of Sciences of the Czech Republic, Zitna 25, 115 67 Prague 1, Czech Republic |
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Abstract: | We prove that the finite element method for one-dimensional problems yields no discretization error at nodal points provided the shape functions are appropriately chosen. Then we consider a biharmonic problem with mixed boundary conditions and the weak solution u. We show that the Galerkin approximation of u based on the so-called biharmonic finite elements is independent of the values of u in the interior of any subelement. |
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Keywords: | boundary value elliptic problems finite element method generalized splines elastic plate |
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