High-order accurate discontinuous finite element solution of the 2D Euler equations
Journal of Computational Physics
Multilevel algorithms for generating coarse grids for multigrid methods
Proceedings of the 2001 ACM/IEEE conference on Supercomputing
High-order accurate implementation of solid wall boundary conditions in curved geometries
Journal of Computational Physics
Journal of Computational Physics
libMesh: a C++ library for parallel adaptive mesh refinement/coarsening simulations
Engineering with Computers
Polymorphic nodal elements and their application in discontinuous Galerkin methods
Journal of Computational Physics
Computers & Mathematics with Applications
Error estimation and anisotropic mesh refinement for 3d laminar aerodynamic flow simulations
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.45 |
In this work we show that the flexibility of the discontinuous Galerkin (dG) discretization can be fruitfully exploited to implement numerical solution strategies based on the use of elements with very general shapes. Thanks to the freedom in defining the mesh topology, we propose a new h-adaptive technique based on agglomeration coarsening of a fine mesh. The possibility to enhance the error distribution over the computational domain is investigated on a Poisson problem with the goal of obtaining a mesh independent discretization. The main building block of our dG method consists of defining discrete polynomial spaces directly on physical frame elements. For this purpose we orthonormalize with respect to the L^2-product a set of monomials relocated in a specific element frame and we introduce an easy way to reduce the cost related to numerical integration on agglomerated meshes. To complete the dG formulation for second order problems, two extensions of the BR2 scheme to arbitrary polyhedral grids, including an estimate of the stabilization parameter ensuring the coercivity property, are here proposed.