多边形区域上热传导方程的Legendre-Chebyshev谱元法

Legendre-Chebyshev spectral element method for heat conduction equations on polygonal domain

建立了多边形区域上热传导方程的Legendre-Chebyshev谱元法,通过把多边形区域剖分成一些互不相交的凸四边形子区域,在各个子区域上采用Legendre-Galerkin方法,右端项采用Chebyshev插值逼近,计算可并行实现,给出了方法的稳定性和收敛性分析.数值算例显示了方法的有效性.

The Legendre-Chebyshev spectral element method is developed to solve the heat conduction equations on the polygonal domain. By partitioning the domain into convex quadrangle subdomains, the scheme is formulated in the Legendre-Galerkin form, but the term on the right-hand side is approximated by the Chebyshev collocation method. The method can be implemented in parallel.The stability and the convergence of the method are proved. Numerical examples show the efficiency of the method.