@Article{AAMM-4-2,
author = {Li, Kun},
title = {The Eulerian-Lagrangian Method with Accurate Numerical Integration},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2012},
volume = {4},
number = {2},
pages = {156--174},
abstract = {<p style="text-align: justify;">This paper is devoted to the study of the Eulerian-Lagrangian method
(ELM) for convection-diffusion equations on unstructured grids with or without
accurate numerical integration. We first propose an efficient and accurate algorithm
to calculate the integrals in the Eulerian-Lagrangian method. Our approach
is based on an algorithm for finding the intersection of two non-matching grids. It
has optimal algorithmic complexity and runs fast enough to make time-dependent
velocity fields feasible. The evaluation of the integrals leads to increased precision
and the unconditional stability. We demonstrate by numerical examples that the
ELM with our proposed algorithm for accurate numerical integration has the following
two features: firstly, it is much more accurate and more stable than the ones
with traditional numerical integration techniques and secondly, the overall cost of
the proposed method is comparable with the traditional ones.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.11-m1192},
url = {https://global-sci.com/article/73535/the-eulerian-lagrangian-method-with-accurate-numerical-integration}
}