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Quadrature for hp-Galerkin BEM in R³
(1996)SAM Research ReportThe Galerkin discretization of a Fredholm integral equation of the second kind on a closed, piecewise analytic surface $\Gamma \subset \hbox {R}^3$ is analyzed. High order, $hp$-boundary elements on grids which are geometrically graded toward the edges and vertices of the surface give exponential convergence, similar to what is known in the $hp$ Finite Element Method. A quadrature strategy is developed which gives rise to a fully discrete ...Report -
On coupled problems for viscous flow in exterior domains
(1996)SAM Research ReportThe use of the complete Navier-Stokes system in an unbounded domain is not always convenient in computations and, therefore, the Navier-Stokes problem is often truncated to a bounded domain. In this paper we simulate the interaction between the flow in this domain and the exterior flow with the aid of a coupled problem. We propose in particular a linear approximation of the exterior flow (here the Stokes flow or potential flow) coupled ...Report -
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