本刊英文版2014年57卷第2期摘要(英文)

New schemes with fractal error compensation for PDE eigenvalue computations SUN JiaChang Abstract With an error compensation term in the fractal Rayleigh quotient of PDE eigen-problems,we propose a new scheme by perturbing the mass matrix Mhto Mh=Mh+Ch2mKh,where Khis the corresponding stif matrix of a 2m 1 degree conforming fnite element with mesh size h for a 2m-order self-adjoint PDE,and the constant C exists in the priority error estimationλh jλj^Ch2mλ2j.In particular,for Laplace eigen-problems over regular domains in uniform mesh,e.g.,cube,equilateral triangle and regular hexagon,etc.,we fnd

New schemes with fractal error compensation for PDE eigenvalue computations;Abelianness of the ＂missing part＂ from a sheaf category to a module category;Totally compatible associative and Lie dialgebras, tridendriform algebras and PostLie algebras