Subcell finite volume multigrid preconditioning for high-order discontinuous Galerkin methods

Multigrid algorithms for high order discontinuous Galerkin methods

I n this paper we study the performance of hand p-multigrid algorithms for high order Discontinuous Galerkin discretizations of elliptic problems. We test the performance of the multigrid schemes employing a wide class of smoothers and considering both twoand three-dimensional test cases.

High-Order Discontinuous Galerkin Methods using a Spectral Multigrid Approach

High Order Finite Difference and Finite Volume WENO Schemes and Discontinuous Galerkin Methods for CFD

In recent years high order numerical methods have been widely used in computational uid dynamics (CFD), to e ectively resolve complex ow features using meshes which are reasonable for today's computers. In this paper we review and compare three types of high order methods being used in CFD, namely the weighted essentially non-oscillatory (WENO) nite di erence methods, the WENO nite volume metho...

High-Order Discontinuous Galerkin Methods for CFD

In recent years it has become clear that the current computational methods for scientific and engineering phenomena are inadequate for many challenging problems. Examples of these problems are wave propagation, turbulent fluid flow, as well as problems involving nonlinear interactions and multiple scales. This has resulted in a significant interest in so-called high-order accurate methods, whic...

Dispersive Behaviour of High Order Discontinuous Galerkin Finite Element Methods

The dispersive properties of hp version discontinuous Galerkin finite element approximation are studied in three different limits. For the small wave-number limit hk → 0, we show the discontinuous Galerkin gives a higher order of accuracy than the standard Galerkin procedure, thereby confirming the conjectures of Hu and Atkins (J. Comput. Phys., 182(2):516– 545, 2002 ). If the mesh is fixed and...