贵州师范大学数学科学学院;
针对圆域上四阶变系数问题，提出了一种基于降阶格式的Legendre-Fourier谱方法。首先，借助极坐标变换和辅助函数，将原问题转化为极坐标系下的二阶耦合系统，并根据极条件定义一类带权的Sobolev空间，建立其变分形式及其离散。然后，在适当的条件下，证明了弱解及数值解的存在性与唯一性，再结合Céa引理和非一致带权Sobolev空间中投影算子的逼近性质，弱解与数值解之间的误差估计进一步被推导。最后，通过数值实验对算法进行了验证，实验结果表明所提出的离散格式的算法设计具有谱精度。
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基本信息:
DOI：
中图分类号:O241.8
引用信息:
[1]杨青青,安静.四阶变系数问题基于降阶格式的Legendre-Fourier谱逼近[J].山东师范大学学报(自然科学版),2025,40(01):52-63.
基金信息:
国家自然科学基金资助项目(12461078); 贵州省教育厅自然科学研究资助项目(黔教技[2023]011)