Agglomeration-based physical frame dG discretizations: An attempt to be mesh free

作者：Bassi Francesco; Botti Lorenzo^*; Colombo Alessandro

来源：Mathematical Models and Methods in Applied Sciences, 2014, 24(8): 1495-1539.

DOI：10.1142/S0218202514400028

• Discontinuous Galerkin
• polygonal elements
• polyhedral elements
• arbitrarily shaped elements
• agglomeration
• multigrid

In this work we consider agglomeration-based physical frame discontinuous Galerkin (dG) discretization as an effective way to increase the flexibility of high-order finite element methods. The mesh free concept is pursued in the following (broad) sense: the computational domain is still discretized using a mesh but the computational grid should not be a constraint for the finite element discretization. In particular the discrete space choice, its convergence properties, and even the complexity of solving the global system of equations resulting from the dG discretization should not be influenced by the grid choice. Physical frame dG discretization allows to obtain mesh-independent h-convergence rates. Thanks to mesh agglomeration, high-order accurate discretizations can be performed on arbitrarily coarse grids, without resorting to very high-order approximations of domain boundaries. Agglomeration-based h-multigrid techniques are the obvious choice to obtain fast and grid-independent solvers. These features (attractive for any mesh free discretization) are demonstrated in practice with numerical test cases.

• 出版日期2014-7