@Article{NMTMA-14-4,
author = {Ruo, Li and Yang, Fanyi},
title = {A Sequential Least Squares Method for Elliptic Equations in Non-Divergence Form},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2021},
volume = {14},
number = {4},
pages = {1042--1067},
abstract = {<p style="text-align: justify;">We develop a new least squares method for solving the second-order elliptic equations in non-divergence form. Two least-squares-type functionals are proposed for solving the equation in two sequential steps. We first obtain a numerical
approximation to the gradient in a piecewise irrotational polynomial space. Then
together with the numerical gradient, we seek a numerical solution of the primitive
variable in the continuous Lagrange finite element space. The variational setting
naturally provides an a posteriori error which can be used in an adaptive refinement
algorithm. The error estimates under the $L^2$ norm and the energy norm for both
two unknowns are derived. By a series of numerical experiments, we verify the
convergence rates and show the efficiency of the adaptive algorithm.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.OA-2021-0042},
url = {https://global-sci.com/article/90330/a-sequential-least-squares-method-for-elliptic-equations-in-non-divergence-form}
}