TY - JOUR
T1 - An Error Estimate of a Eulerian-Lagrangian Localized Adjoint Method for a Space-Fractional Advection Diffusion Equation
AU - Wang , Tingting
AU - Li , Xiaofan
AU - Wang , Hong
JO - International Journal of Numerical Analysis and Modeling
VL - 2
SP - 151
EP - 171
PY - 2020
DA - 2020/02
SN - 17
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/13645.html
KW - Space-fractional advection diffusion, fractional Laplacian, characteristic method, error estimate, superdiffusive transport.
AB - <p style="text-align: justify;">We derive a Eulerian-Lagrangian localized adjoint method (ELLAM) for a space-fractional advection diffusion equation that includes a fractional Laplacian operator for modeling
such application as a superdiffusive advective transport. The method symmetrizes the numerical
scheme and generates accurate numerical solutions even if large time steps and relatively coarse
grid meshes are used. We also study the structure of the stiffness matrix to further reduce the
computational complexity and memory requirement. We prove an error estimate for the ELLAM.
Numerical experiments are presented to show the potential of the method.</p>