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boundary value elliptic problems; finite element method; generalized splines; elastic plate
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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