@Article{NMTMA-14-1042, author = {Li , Ruo 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 = {

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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2021-0042 }, url = {http://global-sci.org/intro/article_detail/nmtma/19529.html} }