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Title: On exact results in the finite element method (English)
Author: Hlaváček, Ivan
Author: Křížek, Michal
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940 (print)
ISSN: 1572-9109 (online)
Volume: 46
Issue: 6
Year: 2001
Pages: 467-478
Summary lang: English
Category: math
Summary: 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. (English)
Keyword: boundary value elliptic problems
Keyword: finite element method
Keyword: generalized splines
Keyword: elastic plate
MSC: 35J40
MSC: 65N30
idZBL: Zbl 1066.65126
idMR: MR1865517
DOI: 10.1023/A:1013716729409
Date available: 2009-09-22T18:08:06Z
Last updated: 2020-07-02
Stable URL:
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