TY - JOUR
T1 - Multidomain Legendre-Galerkin Least-Squares Method for  Linear Differential Equations with Variable Coefficients
AU - Qin , Yonghui
AU - Chen , Yanping
AU - Huang , Yunqing
AU - Ma , Heping
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 3
SP - 665
EP - 688
PY - 2020
DA - 2020/03
SN - 13
DO - http://doi.org/10.4208/nmtma.OA-2019-0015
UR - https://global-sci.org/intro/article_detail/nmtma/15780.html
KW - Variable coefficient, Legendre Galerkin, Legendre/Chebyshev-Gauss-Lobatto, least squares.
AB - <p style="text-align: justify;">The multidomain Legendre-Galerkin least-squares method is developed for solving linear differential problems with variable coefficients. By introducing a flux, the original differential equation is rewritten into an equivalent first-order system, and the Legendre Galerkin is applied to the discrete form of the corresponding least squares function. The proposed scheme is based on the Legendre-Galerkin method, and the Legendre/Chebyshev-Gauss-Lobatto collocation method is used to deal with the variable coefficients and the right hand side terms. The coercivity and continuity of the method are proved and the optimal error estimate in $H^1$-norm is obtained. Numerical examples are given to validate the efficiency and spectral accuracy of our scheme. Our scheme is also applied to the numerical solutions of the parabolic problems with discontinuous coefficients and the two-dimensional elliptic problems with piecewise constant coefficients, respectively.</p>