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The hp finite element method for problems in mechanics with boundary layers
(1996)SAM Research ReportWe consider the numerical approximation of boundary layer phenomena occuring 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 exisiting, commercial emp/em and emhp/em finite element (FE) version codes. We show that if high order, "spectral" elements are available, then just two elements are sufficient to approximate ...Report -
Mixed hp Finite Element Methods for Stokes and Non-Newtonian Flow
(1997)SAM Research ReportWe analyze the stability of hp finite elements for viscous incompressible flow. For the classical velocity-pressure formulation, we give new estimates for the discrete inf-sup constants on geometric meshes which are explicit in the polynomial degree k of the elements. In particular, we obtain new bounds for p-elements on triangles. For the three-field Stokes problem describing linearized non-Newtonian flow, we estimate discrete inf-sup ...Report