报告时间：2026年7月5日 上午15:00-16:00

报告地点：逸夫楼1537

报告人：张浩楠 博士 （中国科学院软件研究所）

报告题目：Error estimate of spectral method for steady neutron transport equation

报告摘要：In this talk, we propose a spectral $S_N$ method for the steady-state neutron transport equation in two and three spatial dimensions, using tensor-product spectral discretization in space and product-type quadrature nodes on the unit disk or unit sphere for the angular variable. The key difficulty is that standard polynomial spaces (in 2D) and spherical harmonic spaces (in 3D) cannot simultaneously support interpolation at these nodes, norm equivalence, and optimal error bounds. To resolve this, we construct extended disk polynomial spaces and extended spherical harmonic spaces whose dimensions match the number of quadrature nodes. On these spaces, we prove discrete-continuous $L^2$ norm equivalence, establish stable interpolation operators, and derive optimal $L^2$ interpolation errors. These angular results allow us to prove well-posedness of the fully discrete scheme and obtain optimal $L^2$ error estimates for the numerical solution. Numerical experiments confirm the theoretical convergence rates on representative test problems.