A stabilized hp-Finite Element Method (FEM) of Galerkin Least Squares (GLS) type is analyzed for the Stokes equations in polygonal domains. Contrary to the standard Galerkin FEM, this method admits equal-order interpolation in the velocity and the pressure, which is very attractive from an implementational point of view. In conjunction with geometrically refined meshes and linearly increasing approximation orders it is shown that thehp-GLSFEM ...

We analyze an hp FEM for convection-diffusion problems. Stability is achieved by suitably upwinded test functions, generalizing the classical $\alpha$-quadratically upwinded and the Hemker test-functions for piecewise linear trial spaces (see, e.g., [12] and the references there). The method is proved to be stable independently of the viscosity. Further, the stability is shown to depend only weakly on the spectral order. We show how ...

This paper is devoted to the a priori and a posteriori error analysis of the hp-version of the discontinuous Galerkin finite element method for partial differential equations of hyperbolic and nearly-hyperbolic character. We consider second-order partial differential equations with nonnegative characteristic form, a large class of equations which includes convection-dominated diffusion problems, degenerate elliptic equations and second-order ...

When standard boundary element methods (BEM) are used to solve the linearized vector Molodensky problem we are confronted with two problems: (i) the absence of $O(|x|^{-2})$ terms in the decay condition is not taken into account, since the single layer ansatz, which is commonly used as representation of the perturbation potential, is of the order $O(|x|^{-1})$ as $x \to \infty$. This implies that the standard theory of Galerkin BEM is not ...

We 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 ...