邊界補償法求解熱方程

Abstract

利用擬譜法並且施加邊界條件逼近熱方程式。在這份論文之中，可以利用離散能量估計確定邊界條件的懲罰參數。我們利用已知正解的齊次熱方程式及非齊次熱方程式做數值計算，並與預期的準確性相符合。

A method to impose boundary conditions for pseudospectral approximations to heat equations is suggested. In this study, the boundary conditions are weakly enforced to the scheme with the penalty parameters which are determined analytically by using the discrete energy estimate. Numerical experiments based on the proposed scheme are performed including homogeneous heat equations and inhomogeneous heat equations where exact solutions exist, and the numerical results show that the accuracy as we expected.