@Article{AAMM-9-2,
author = {Li, Hu and Jin, Huang},
title = {A High-Accuracy Mechanical Quadrature Method for Solving the Axisymmetric Poisson's Equation},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2017},
volume = {9},
number = {2},
pages = {393--406},
abstract = {<p style="text-align: justify;">In this article, we consider the numerical solution for Poisson&#39;s equation in
axisymmetric geometry. When the boundary condition and source term are axisymmetric,
the problem reduces to solving Poisson&#39;s equation in cylindrical coordinates in
the two-dimensional ($r,z$) region of the original three-dimensional domain $S$. Hence,
the original boundary value problem is reduced to a two-dimensional one. To make
use of the Mechanical quadrature method (MQM), it is necessary to calculate a particular
solution, which can be subtracted off, so that MQM can be used to solve the resulting
Laplace problem, which possesses high accuracy order $\mathcal{O}$($h^3_{max}$) and low computing
complexities. Moreover, the multivariate asymptotic error expansion of MQM
accompanied with $\mathcal{O}$($h^3_i$) for all mesh widths $h_i$ is got. Hence, once discrete equations
with coarse meshes are solved in parallel, the higher accuracy order of numerical approximations
can be at least $\mathcal{O}$($h^5_{max}$) by the splitting extrapolation algorithm (SEA).
Meanwhile, a posteriori asymptotic error estimate is derived, which can be used to
construct self-adaptive algorithms. The numerical examples support our theoretical
analysis.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.2015.m1287},
url = {https://global-sci.com/article/73257/a-high-accuracy-mechanical-quadrature-method-for-solving-the-axisymmetric-poissons-equation}
}