TY - JOUR
T1 - Stability Analysis and Error Estimates of Local Discontinuous Galerkin Method for Convection-Diffusion Equations on Overlapping Mesh with Non-Periodic Boundary Conditions
AU - Chuenjarern , Nattaporn
AU - Wuttanachamsri , Kanognudge
AU - Yang , Yang
JO - International Journal of Numerical Analysis and Modeling
VL - 6
SP - 788
EP - 810
PY - 2021
DA - 2021/11
SN - 18
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/19950.html
KW - Local discontinuous Galerkin method, stability, error analysis, overlapping meshes.
AB - <p style="text-align: justify;">A new local discontinuous Galerkin (LDG) method for convection-diffusion equations
on overlapping meshes with periodic boundary conditions was introduced in [14]. With the new
method, the primary variable $u$ and the auxiliary variable $p = u_x$ are solved on different meshes. In
this paper, we will extend the idea to convection-diffusion equations with non-periodic boundary
conditions, i.e. Neumann and Dirichlet boundary conditions. The main difference is to adjust
the boundary cells. Moreover, we study the stability and suboptimal error estimates. Finally,
numerical experiments are given to verify the theoretical findings.</p>