This paper proposes and analyzes a class of robust globally divergence-free weak Galerkin (WG) finite element methods for Stokes equations. The new methods use the Pk/Pk−1 (k ≥ 1) discontinuous finite element combination for velocity and pressure in the interior of elements, and piecewise Pl/Pk (l = k − 1, k) for the trace approximations of the velocity and pressure on the inter-element boundar...

H E amount of selection pressure applied on the phenotypic level to T metric characters can be expressed in terms of the selection differential, defined as the extent of superiority of the individuals which are the parents of the next generation (weighted for the relative number of offspring they produce) over the average of their own generation. For characters showing a discontinuous distribut...

In this note we propose a finite element method for incompressible (or compressible) elasticity problems with discontinuous modulus of elasticity (or, if compressible, Poisson’s ratio). The problem is written on mixed form using P 1–continuous displacements and the space of piecewise P 0 pressures, leading to the possibility of eliminating the pressure beforehand in the compressible case. In th...

Editor’s key points † Continuous measurement of beat-to-beat arterial pressure (AP) during the dynamic phases of anaesthesia facilitates recognition and treatment of acute variations. † The non-invasive AP monitor NexfinTM was compared with invasive AP (IAP) measurements during induction of anaesthesia. † NexfinTM reliably and quickly detected acute changes in AP, but its accuracy was insuffici...

In this article, we analyze several discontinuous Galerkin methods (DG) for the Stokes problem under the minimal regularity on the solution. We assume that the velocity u belongs to [H 0 (Ω)] d and the pressure p ∈ L0(Ω). First, we analyze standard DG methods assuming that the right hand side f belongs to [H−1(Ω) ∩ L(Ω)]. A DG method that is well defined for f belonging to [H−1(Ω)]d is then inv...

Editor’s key points † Continuous measurement of beat-to-beat arterial pressure (AP) during the dynamic phases of anaesthesia facilitates recognition and treatment of acute variations. † The non-invasive AP monitor NexfinTM was compared with invasive AP (IAP) measurements during induction of anaesthesia. † NexfinTM reliably and quickly detected acute changes in AP, but its accuracy was insuffici...

The three-dimensional jump conditions for the pressure and velocity fields, up to the second normal derivative, across an incompressible/inextensible interface in the Stokes regime are derived herein. The fluid viscosity is only piecewise continuous in the domain while the embedded interface exerts singular forces on the surround fluids. This gives rise to discontinuous solutions in the pressur...

We introduce and analyze a discontinuous Galerkin method for the incompressible Navier-Stokes equations that is based on finite element spaces of the same polynomial order for the approximation of the velocity and the pressure. Stability of this equal-order approach is ensured by a pressure stabilization term. A simple element-by-element postprocessing procedure is used to provide globally dive...

We consider residual-based stabilised finite element methods for the generalised Oseen problem. The unique solvability based on a modified stability condition and an error estimate are proved for inf-sup stable discretisations of velocity and pressure. The analysis highlights the role of an additional stabilisation of the incompressibility constraint. It turns out that the stabilisation terms o...