Geodesic
On exact results in the finite element method
Applications of Mathematics, Tome 46 (2001) no. 6, pp. 467-478.

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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.
DOI : 10.1023/A:1013716729409
Classification : 35J40, 65N30
Keywords: boundary value elliptic problems; finite element method; generalized splines; elastic plate 
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Hlaváček, Ivan; Křížek, Michal. On exact results in the finite element method. Applications of Mathematics, Tome 46 (2001) no. 6, pp. 467-478. doi : 10.1023/A:1013716729409. http://geodesic.mathdoc.fr/articles/10.1023/A:1013716729409/

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