Ivan Hlavacek, Michal Krizek, Mathematical Institute, Academy of Sciences of the Czech Republic, Zitna 25, 115 67 Prague 1, Czech Republic, e-mail: krizek@math.cas.cz
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.
Keywords: boundary value elliptic problems, finite element method, generalized splines, elastic plate
Classification (MSC 2000): 65N30
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