AI 中文总结
针对福克 - 普朗克型方程，提出最小二乘弱伽辽金有限元方法，利用最小二乘公式应对非光滑扩散张量问题，设计数值格式并给出理论基础，经数值实验验证其稳健性和性能。
AI 中文摘要
本文提出了一种用于一类二阶福克 - 普朗克型椭圆方程的最小二乘弱伽辽金（LS - WG）有限元方法。为应对非光滑扩散张量带来的数值挑战，该方法采用最小二乘公式得到对称正定离散系统。通过局部构造弱二阶偏导数和弱散度设计数值格式，给出严格理论基础，包括离散解唯一性及离散能量范数下的最优阶误差估计。最后通过大量数值实验验证理论结果，展示该数值格式的稳健性和性能。
英文摘要
This paper presents a least squares weak Galerkin (LS-WG) finite element method for a class of second order elliptic equations of Fokker-Planck type. To address the numerical challenges arising from non-smooth diffusion tensors, the proposed method utilizes a least-squares formulation that yields a symmetric positive definite (SPD) discrete system. The numerical scheme is designed by employing locally constructed weak second order partial derivatives and the weak divergence commonly used within the weak Galerkin framework. A rigorous theoretical foundation is provided, establishing the uniqueness of the discrete solution and deriving optimal-order error estimates in a discrete energy norm. Finally, extensive numerical experiments are reported to validate the theoretical findings and demonstrate the robustness and performance of the numerical scheme.
Comments18 pages,8 tables, 4 figures
