A sequential least squares method for elliptic equations in non-divergence form
Abstract
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 equations in two steps. We first obtain a numerical approximation to the gradient in a piecewisely irrotational polynomial space. Then together with the numerical gradient, we seek a numerical solution of the primitive variable in continuous finite element space. The variational setting naturally provides a posteriori error which could be used in an adaptive refinement algorithm. The error estimates in norm and energy norms 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.
Cite
@article{arxiv.1906.03754,
title = {A sequential least squares method for elliptic equations in non-divergence form},
author = {Ruo Li and Fanyi Yang},
journal= {arXiv preprint arXiv:1906.03754},
year = {2020}
}