摘要
本文研究了简支板边界条件下四阶问题基于降阶格式的一种有效的谱Galerkin逼近.通过引入一个辅助函数和适当的Sobolev空间,将原问题化为两个耦合的二阶问题,建立其弱形式和相应的离散格式,利用Lax-Milgram定理和投影算子的逼近性质,我们证明了弱解和逼近解的存在唯一性以及它们之间的误差估计.再利用Legendre多项式的正交性质构造了一组适当的基函数,推导了离散格式基于张量积的矩阵形式.最后,我们给出了一些数值算例,数值结果验证了算法的有效性和理论结果的正确性.
In this paper,we study an ecient spectral-Galerkin approximation for fourth-order equation with simply supported plate boundary conditions.By introducing an auxiliary function and some appropriate Sobolev spaces,reducing the fourth-order problem to two coupled second-order problems,establishing the associated weak form and discrete scheme,using Lax-Milgram theorem and the approximation properties of projection operator,we prove the existence and uniqueness of the weak solutions and approximation solutions and the error estimation between them.Next,by using the orthogonality of Legendre polynomials,we construct a set of appropriate basis functions and derive the matrix formulations based on the tensor-product.Finally,some numerical experiments are carried out to validate the eciency of the algorithm and the correctness of the theoretical results.
作者
覃嘉淇
安静
QIN Jia-qi;AN Jing(School of Mathematical Sciences,Guizhou Normal University,Guizhou 550025,China)
出处
《数学杂志》
2023年第5期433-446,共14页
Journal of Mathematics
基金
国家自然科学基金项目(11661022)
贵州省科技计划项目(黔科合平台人才[2017]5726-39)
贵州师范大学学术新苗基金项目(黔师新苗[2021]A04号)。
关键词
四阶问题
简支板边界条件
降阶格式
谱方法
误差估计
fourth-order problem
boundary conditions of simple support plate
reduced format
spectral method
error estimation
