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Approximation theory for the hp -version finite element method and application to the non-linear Laplacian

✍ Scribed by Mark Ainsworth; David Kay

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 155 KB
Volume: 34
Category: Article
ISSN: 0168-9274
DOI: 10.1016/s0168-9274(99)00040-9

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✦ Synopsis

The non-linear Laplacian involves the differential equation

and Ω is a polygonal domain. The classical error estimates for the h version finite element approximation are generalized to the hp version, when applied to locally quasi-uniform meshes of quadrilateral elements. The estimates are expressed as an explicit function of the mesh-size h and the order p of the elements. The estimates include the case when the solution belongs to a Sobolev class and also when the solution has algebraic singularities due to the geometry of the domain.

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