A high-order fictitious-domain method for the advection-diffusion equation on time-varying domain

04/05/2021 ∙ by Chuwen Ma, et al. ∙ 0

We develop a high-order finite element method to solve the advection-diffusion equation on a time-varying domain. The method is based on a characteristic-Galerkin formulation combined with the k^ th-order backward differentiation formula (BDF-k) and the fictitious-domain finite element method. Optimal error estimates of the discrete solutions are proven for 2≤ k≤ 4 by taking account of the errors from interface-tracking, temporal discretization, and spatial discretization, provided that the (k+1)^ th-order Runge-Kutta scheme is used for interface-tracking. Numerical experiments demonstrate the optimal convergence of the method for k=3 and 4.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.