高波数Helmholtz方程的高阶连续多罚有限元方法的稳定性估计（英文）

Stability Estimates of High Order Continuous Interior Multi-Penalty Finite Element Method for Helmholtz Equation with High Wave Number

本文考虑二维和三维区域上高波数Helmholtz散射问题的高阶(多项式次数p≥2)连续多罚有限元方法.本文证明在加罚参数的虚部大于零的条件下,对任意k, h, p,连续多罚有限元方法是绝对稳定的,即都存在唯一解.这里k是波数, h为网格尺寸.

Some continuous interior multi-penalty finite element method(CMP-FEM)of using piecewise polynomials of order p 2 for the Helmholtz equation in the two and three dimensions is considered.The proposed CMP-FEM is stable(hence well-posed)for any k,h,p and penalty parameters with positive imaginary parts,where k is the wave number,h is the mesh size.