Abstract
In general, a finite element method (FEM) for fourth-order problems requires trial and test functions belonging to subspaces of the Sobolev space H 2(Ω), and this would require C 1 −elements, i.e., piecewise polynomials which are C 1 across interelement boundaries. In order to avoid this requirement we will use nonconforming Zienkiewicz-type (Z-type) triangle applied to biharmonic problem. We propose a new approach to prove the order of convergence by comparison to suitable modified Hermite triangular finite element. This method is more natural and it could be also applied to the corresponding fourth-order eigenvalue problem. Some computational aspects are discussed and numerical example is given.
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Andreev, A.B., Racheva, M.R. (2010). Zienkiewicz-Type Finite Element Applied to Fourth-Order Problems. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2009. Lecture Notes in Computer Science, vol 5910. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12535-5_82
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DOI: https://doi.org/10.1007/978-3-642-12535-5_82
Publisher Name: Springer, Berlin, Heidelberg
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