Abstract. A new residual local projection stabilized method (RELP) is proposed as a result of an enriched Petrov-Galerkin strategy for the Oseen problem. The P 1 × Pl pairs, l = 0, 1 with continuous or discontinuous pressures, are made stable by enhancing them with solutions of residual-based local Oseen problems and performing a static condensation procedure afterward. This process does not in...

Abstract Over the past two decades, there has been much development in discontinuous Galerkin methods for incompressible flows and compressible with a positive Mach number, but almost no attention paid to variable-density at low speeds. This paper presents pressure-based method flow low-Mach number limit. We use pressure correction method, which is simplified by solving mass flux instead of vel...

High-order polynomial approximations of discontinuous functions give rise to oscillations in the vicinity of the discontinuity known as Gibbs phenomenon. Enrichment of the basis using discontinuous functions is shown to remove these oscillations and to recover the convergence properties generally associated with the spectral approximation of smooth functions. The convergence properties of the e...

In several materials, unconventional superconductivity appears nearby a quantum phase transition where long-range magnetic order vanishes as a function of a control parameter like charge doping, pressure or magnetic field. The nature of the quantum phase transition is of key relevance, because continuous transitions are expected to favour superconductivity, due to strong fluctuations. Discontin...

We introduce a new mixed discontinuous/continuous Galerkin finite element for solving the 2and 3-dimensional wave equations and equations of incompressible flow. The element, which we refer to as P1DG-P2, uses discontinuous piecewise linear functions for velocity and continuous piecewise quadratic functions for pressure. The aim of introducing the mixed formulation is to produce a new flexible ...

Two discrete functional analysis tools are established for spaces of piecewise polynomial functions on general meshes: (i) a discrete counterpart of the continuous Sobolev embeddings, in both Hilbertian and non-Hilbertian settings; (ii) a compactness result for bounded sequences in a suitable Discontinuous Galerkin norm, together with a weak convergence property for some discrete gradients. The...

For Stokes equations with a discontinuous viscosity across an arbitrary interface or/and singular forces along the interface, it is known that the pressure is discontinuous and the velocity is non-smooth. It has been shown that these discontinuities are coupled together, which makes it difficult to obtain accurate numerical solutions. In this paper, a new numerical method that decouples the jum...