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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Bibliographic Details
Published in:Computer methods in applied mechanics and engineering Vol. 157; no. 3; pp. 311 - 333
Main Authors: Schwab, C., Suri, M., Xenophontos, C.
Format: Journal Article Conference Proceeding
Language:English
Published: Amsterdam Elsevier B.V 11.05.1998
Elsevier
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:0045-7825
1879-2138
DOI:10.1016/S0045-7825(97)00243-0