TY - JOUR
T1 - A Direct Discontinuous Galerkin Method for Time Fractional Diffusion Equations with Fractional Dynamic Boundary Conditions
AU - Zhao , Jingjun
AU - Zhao , Wenjiao
AU - Xu , Yang
JO - Journal of Computational Mathematics
VL - 1
SP - 156
EP - 177
PY - 2023
DA - 2023/12
SN - 42
DO - http://doi.org/10.4208/jcm.2203-m2021-0233
UR - https://global-sci.org/intro/article_detail/jcm/22156.html
KW - Time fractional diffusion equation, Numerical stability, Convergence.
AB - <p style="text-align: justify;">This paper deals with the numerical approximation for the time fractional diffusion
problem with fractional dynamic boundary conditions. The well-posedness for the weak
solutions is studied. A direct discontinuous Galerkin approach is used in spatial direction
under the uniform meshes, together with a second-order Alikhanov scheme is utilized in
temporal direction on the graded mesh, and then the fully discrete scheme is constructed.
Furthermore, the stability and the error estimate for the full scheme are analyzed in detail.
Numerical experiments are also given to illustrate the effectiveness of the proposed method.</p>