@Article{IJNAM-16-5,
author = {Zhaonan, Dong},
title = {Discontinuous Galerkin Methods for the Biharmonic Problem on Polygonal and Polyhedral Meshes},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2019},
volume = {16},
number = {5},
pages = {825--846},
abstract = {<p style="text-align: justify;">We introduce an $hp$-version symmetric interior penalty discontinuous Galerkin finite
element method (DGFEM) for the numerical approximation of the biharmonic equation on general
computational meshes consisting of polygonal/polyhedral (polytopic) elements. In particular, the
stability and $hp$-version a-priori error bound are derived based on the specific choice of the interior
penalty parameters which allows for edges/faces degeneration. Furthermore, by deriving a new
inverse inequality for a special class of polynomial functions (harmonic polynomials), the proposed
DGFEM is proven to be stable to incorporate very general polygonal/polyhedral elements with
an $arbitrary$ number of faces for polynomial basis with degree $p$ = 2, 3. The key feature of the
proposed method is that it employs elemental polynomial bases of total degree $\mathcal{P}$<sub>$p$</sub>, defined in the
physical coordinate system, without requiring the mapping from a given reference or canonical
frame. A series of numerical experiments are presented to demonstrate the performance of the
proposed DGFEM on general polygonal/polyhedral meshes.</p>},
issn = {2617-8710},
doi = {https://doi.org/2019-IJNAM-13256},
url = {https://global-sci.com/article/83097/discontinuous-galerkin-methods-for-the-biharmonic-problem-on-polygonal-and-polyhedral-meshes}
}