数学杂志2024，Vol.44Issue(3)：269-282,14.
椭圆域上二阶/四阶变系数问题有效的谱Galerkin逼近
EFFECTIVE SPECTRAL GALERKIN APPROXIMATION FOR SECOND-ORDER/FOURTH-ORDER VARIABLE COEFFICIENT PROBLEMS IN AN ELLIPTIC DOMAIN
摘要
Abstract
In this paper,we propose an efficient spectral Galerkin approximation for second-order/fourth-order problems with variable coefficients in an elliptic domain.First,we convert the initial problem into an equivalent form in polar coordinates.Subsequently,we establish the weak form and corresponding discrete scheme.Secondly,we prove the existence and uniqueness of weak and approximate solutions,and we also offer error estimates for the second-order case.In addition,based on the polar condition and the orthogonality of Legendre polynomials,we construct a set of effective radial basis functions,perform a truncated Fourier expansion in the direction of θ,and derive the equivalent matrix form of the discrete scheme.Finally,we provide a large number of numerical examples,and the numerical results show the convergence and spectral accuracy of our algorithm.关键词
二阶/四阶问题/谱Galerkin方法/误差分析/椭圆区域Key words
Second-order/fourth-order problems/spectral Galerkin method/error analysis/elliptic domain分类
数理科学引用本文复制引用
田晓红,安静..椭圆域上二阶/四阶变系数问题有效的谱Galerkin逼近[J].数学杂志,2024,44(3):269-282,14.基金项目
国家自然科学基金资助(12061023),贵州师范大学学术新苗基金资助(黔师新苗[2021]A04号). （12061023）
