Mathematicsisplayinganevermoreimportant…-ical sciences, provoking a blurring of
boundaries between scienti? c disciplines and a resurgence of interest in the modern as …

The analysis of singular perturbed differential equations began early in the twentieth
century, when approximate solutions were constructed from asymptotic expansions …

Many real-world problems are described by partial differential equations whose numerical
solution represents an important part of numerical mathematics. There are several …

In this paper a new local discontinuous Galerkin method for the incompressible stationary
Navier-Stokes equations is proposed and analyzed. Four important features render this …

We present a class of discontinuous Galerkin methods for the incompressible Navier–Stokes
equations yielding exactly divergence-free solutions. Exact incompressibility is achieved by …

Discontinuous Galerkin (DG) methods are a class of finite element methods using
discontinuous basis functions, which are usually chosen as piecewise polynomials. Since …

This paper concerns with numerical approximations of solutions of fully nonlinear second
order partial differential equations (PDEs). A new notion of weak solutions, called moment …

This paper presents the latest developments of a discontinuous Galerkin (DG) method for
incompressible flows introduced in [Bassi F, Crivellini A, Di Pietro DA, Rebay S. An artificial …

In this paper the artificial compressibility flux Discontinuous Galerkin (DG) method for the
solution of the incompressible Navier–Stokes equations has been extended to deal with the …

We devise and analyze a new local discontinuous Galerkin (LDG) method for the Stokes
equations of incompressible fluid flow. This optimally convergent method is obtained by …