In this paper, we develop least-squares finite element methods (LSFEMs) for incompressible fluid flows with improved mass conservation. Specifically, we formulate a new locally conservative LSFEM for the velocity– vorticity–pressure Stokes system, which uses a piecewise divergence-free basis for the velocity and standard C 0 elements for the vorticity and the pressure. The new method, which we ...

Discontinuous Galerkin (DG) and matrix-free finite element methods with a novel projective pressure estimation are combined to enable the numerical modeling of magma dynamics in 2D and 3D using the library deal.II . The physical model is an advection-reaction type system consisting of two hyperbolic equations to evolve porosity and soluble mineral abundance and one elliptic equation to recover ...

In this paper we present a thorough set of numerical experiments to confirm the robustness of several Discontinuous Galerkin (DG) methods proposed for the approximation of Darcy law. We perform fairly twoand three-dimensional tests involving both low and high order approximations. Convergence tests carried out on Cartesian grids as well as on structured and unstructured triangular grids confirm...

We calculate the meniscus location in tapered capillaries under the influence of pressure difference and dielectrophoretic forces with and without gravity. We find that the meniscus location can be a discontinuous function of the pressure difference or the applied voltage and that the meniscus can "jump" to one end or another of the capillary. Phase diagrams are given as a function of the press...