An HDG method using a hybridized numerical flux
Oikawa, Issei
arXiv, 1811.00737 / Harvested from arXiv
Text on arXiv
In this paper, we propose a new hybridizable discontinuous Galerkin (HDG) method for steady-state diffusion problems. In the proposed method, both the trace and flux of the exact solution are hybridized, whereas only the trace is hybridized and the flux is approximated by the numerical flux. We prove that our method is superconvergent if finite element spaces admit the $M$-decomposition. The so-called Lehrenfeld-Sch\"oberl stabilization is implicitly included in our method, so that the orders of convergence in all variables are optimal without postprocessing and computation of any projection if finite element spaces are appropriately chosen. Numerical results are present to validate our theoretical results.
Publié le : 2018-11-02
Classification:  Mathematics - Numerical Analysis 
@article{1811.00737,
     author = {Oikawa, Issei},
     title = {An HDG method using a hybridized numerical flux},
     journal = {arXiv},
     volume = {2018},
     number = {0},
     year = {2018},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1811.00737}
}

Oikawa, Issei. An HDG method using a hybridized numerical flux. arXiv, Tome 2018 (2018) no. 0, . http://gdmltest.u-ga.fr/item/1811.00737/