The hp finite element method for problems in mechanics with boundary layers

We consider the numerical approximation of boundary layer phenomena occurring in many singularly perturbed problems in mechanics, such as plate and shell problems. We present guidelines for the effective resolution of such layers in the context of existing, commercial p and hp finite element (FE) ve...

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Vydáno v:Computer methods in applied mechanics and engineering Ročník 157; číslo 3; s. 311 - 333
Hlavní autoři: Schwab, C., Suri, M., Xenophontos, C.
Médium: Journal Article Konferenční příspěvek
Jazyk:angličtina
Vydáno: Amsterdam Elsevier B.V 11.05.1998
Elsevier
Témata:
Computational techniques
Exact sciences and technology
Finite-element and galerkin methods
Fundamental areas of phenomenology (including applications)
Mathematical methods in physics
Physics
Solid mechanics
Static elasticity
Static elasticity (thermoelasticity...)
Structural and continuum mechanics
Finite element method
Singularity
Shells
Numerical method
Adaptive method
Boundary layers
Plates
ISSN:0045-7825, 1879-2138
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Shrnutí:We consider the numerical approximation of boundary layer phenomena occurring in many singularly perturbed problems in mechanics, such as plate and shell problems. We present guidelines for the effective resolution of such layers in the context of existing, commercial p and hp finite element (FE) version codes. We show that if high order, ‘spectral’ elements are available, then just two elements are sufficient to approximate these layers at a near-exponential rate, independently of the problem parameters thickness or Reynolds number. We present hp mesh design principles for situations where both corner singularities and boundary layers are present.
Bibliografie:SourceType-Scholarly Journals-2
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ObjectType-Conference Paper-1
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ISSN:0045-7825
1879-2138
DOI:10.1016/S0045-7825(97)00243-0