摘要
针对非稳态二维对流扩散反应方程的数值求解,提出一种高次有限元与黄金比例有限差分相结合的全离散化格式.首先,采用高次有限元构造模型方程的空间尺度;其次,建立时间尺度的θ-隐格式代数系统,并选取θ=0.618的黄金分割比例优化计算精度;最后,通过数值计算验证了新格式对于时空间非稳态问题具有高阶稳定的精确收敛结果.
A fully-discretizing scheme combining high high-order finite elements and golden ratio finite difference is presented for the numerical solution of unsteady two-dimensional convection-diffusion reaction equation.Firstly,the spatial scale of the model equation is constructed by using higher-order finite element method.Secondly,a time-scale θ-implicit scheme algebraic system is established,and the golden section ratio of θ=0.618 is selected to optimize the calculation accuracy.Finally,it is shown that in numerical examples the new scheme has obtained higher-order and stable convergence results with great precision for the space-time unsteady problem.
作者
孙美玲
丁晓
江山
SUN Meiling;DING Xiao;JIANG Shan(School of Science,Nantong University,Nantong 226019,China;Department of Public Courses,Nantong Vocational University,Nantong 226007,China)
出处
《扬州大学学报（自然科学版）》
CAS
北大核心
2023年第6期27-33,共7页
Journal of Yangzhou University：Natural Science Edition
基金
国家自然科学基金资助项目(11771224)
南通市基础科学研究指令性资助项目(JC2021123)
南通职业大学自然科学研究重点资助项目(23ZK03)。
关键词
非稳态问题
对流扩散反应方程
高次有限元
黄金比例差分格式
高阶收敛
unsteady problem
convection-diffusion-reaction equation
high-order finite element
golden ratio difference scheme
high-order convergence
