TY - JOUR
T1 - Optimal Error Estimates of the Local Discontinuous Galerkin Method for Willmore Flow of Graphs on Cartesian Meshes
AU - L. Ji & Y. Xu
JO - International Journal of Numerical Analysis and Modeling
VL - 2
SP - 252
EP - 283
PY - 2011
DA - 2011/08
SN - 8
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/685.html
KW - local discontinuous Galerkin method, Willmore flow of graphs, stability, error estimates.
AB - <p style="text-align: justify;">In this paper, we analyze a local discontinuous Galerkin method
for the willmore flow of graphs. We derive the optimal error estimates for
this nonlinear equation in one-dimension and in multi-dimensions for Cartesian
meshes using completely discontinuous piecewise polynomial space with degree
$k \leq 1$.</p>