[PDF] Top 20 Compact and stable discontinuous Galerkin methods for convection diffusion problems

... the compact discontinuous Galerkin 2 (CDG2) method, for solving nonlinear convection-diffusion problems together with a detailed comparison to other well-accepted DG ...scalar ... See full document

... difference methods [4-14, 17-23, ...order compact difference schemes for solving 1D and 2D unsteady convection diffusion equations have been developed [5-10, ...unconditionally stable ... See full document

... The convection-diffusion problems occur in the area of fluid dynamics and several branches of applied ...the convection-diffusion process, transport phenom- ena prevail diffusion, whose effects are ... See full document

... Transient convection diffusion optimal control problems are widely used to model some engineering problems, for example, air pollution problem [, ] and waste water treat- ment ...of problems ... See full document

... the Discontinuous Galerkin Finite Element Method (DGFEM, for short) can be traced back almost half a century ago to the work undertaken on the weak enforcement of Dirichlet boundary conditions for ... See full document

... the diffusion term and we use a “discrete surface” upwind flux to deal with the advection ...test problems exhibiting advection-dominated behaviour, sug- gesting that our surface DG method is stable ... See full document

... particular discontinuous Galerkin FEMs (DGFEMs) requires the im- plementation of inter-element flux terms, which involves combinations of both inner– and outer–traces of the FEM solution, relative to a ... See full document

... In this paper, we discuss the superconvergence of the local discontinuous Galerkin methods for nonlinear convection-diffusion equations. We prove that the numerical solution is (k + ... See full document

... 2. V. Dolejší, M. Feistauer, and J. Hozman: Analysis of semi-implicit DGFEM for nonlinear convection- diffusion problems on nonconforming meshes. Preprint No. MATHknm - 2005/1. Charles University ... See full document

... penalty methods, have typically minimal communication, in the sense that only direct face-element neigh- bours are coupled through the exploitation of appropriate numerical fluxes; this has important advantages ... See full document

... high-order compact scheme in combination precondi- tioner was applied successfully to Diffusion- Convection ...more stable schemes which are efficient with respect to the operation number and ... See full document

... zero. Otherwise, if 𝑓 and 𝒃 are smooth, this term represents a high-order perturbation. In any case the estimator 𝜂 𝐾 is reliable in the sense that the upper bound (3.10) is independent of 𝑕 and 𝜖. Establishing that the ... See full document

... The numerical results presented by the use of the Galerkin Method have proved to be efficient, however, it is noted that the calculation of derivatives the u at each time step should be improved. For this, a first ... See full document

... An alternative is to assume that the solution is harmonic in time. This removes the time derivative from the equation, replacing it with the frequency of the solution instead. The time- harmonic Maxwell equations are ... See full document

... mentwise discontinuous Legendre wavelet approximation, where numerical information only communicates lo- cally via numerical fluxes, to cope with complicated geometries and to represent the dynamics and structure ... See full document

... and discontinuous elements on hybrid meshes involving triangles and quadrangles in two dimensions and tetrahedra, hexahedra and prisms in three ...simple problems with the continuous Galerkin method ... See full document

... The structure of this article is as follows. Section 2 introduces the com- posite finite element spaces, based on the ideas developed in [1, 20, 19]. In Section 3 we introduce the incompressible Navier–Stokes equations ... See full document

... adaptive discontinuous Galerkin finite element methods for the discretization of the bifurcation problem associated with the steady incompressible Navier–Stokes ... See full document

... [16] M. Feistauer, J. Slavik and P. Stupka, “On the Conver- gence of a Combined Finite Volume-Finite Element Me- thod for Nonlinear Convection-Diffusion Problems,” Nu- merical Methods for ... See full document

... gence. In order to overcome this problem, additional interface integral terms are added to the left hand side of () to make the discretization symmetric. For more introduction to the symmetric direct ... See full document