In two and three dimensions, we analyze mixed finite element methods for a velocity-pressure-pseudostress formulation of the Stokes eigenvalue problem. The consist schemes: velocity pressure are approximated with piecewise polynomial, whereas pseudostress consider classic families elements ${H}(\div)$ spaces: Raviart--Thomas Brezzi--Douglas--Marini elements. With aid spectral theory compact ope...

We analyze a new formulation of the Stokes equations in three-dimensional axisymmetric geometries, relying on Fourier expansion with respect to the angular variable: the problem for each Fourier coefficient is two-dimensional and has six scalar unknowns, corresponding to the vector potential and the vorticity. A spectral discretization is built on this formulation, which leads to an exactly div...

A new mixed, stabilized, discontinuous Galerkin formulation for Darcy flow is presented. The formulation combines several attributes not simultaneously satisfied by other methods: It is convergent for any combination of velocity and pressure interpolation higher than first-order, it exactly satisfies a mass balance on each element, and it passes twoand three-dimensional constant-flow ‘‘patch te...

A spinor formulation of the classical Lorentz force is given which describes the presession of an electron’s spin as well as its velocity. Solutions are worked out applicable to an electron in a

3 The hybridizable discontinuous Galerkin (HDG) formulation 3 3.1 HDG local problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3.2 HDG global problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3.3 Local post-process of the velocity field . . . . . . . . . . . . . . . . . . . . 5 3.4 Assembly of the matrices . . . . . . . . . . . . . . . . . . . . . . . . ....

We give a new convergence proof for finite volume schemes approximating scalar conservation laws. The main ingredients of the proof are the kinetic formulation of scalar conservation laws, a discrete entropy inequality, and the velocity averaging technique.