Implicit-explicit BDF k SAV schemes for general dissipative systems and their error analysis

03/10/2021
by   Fukeng Huang, et al.
0

We construct efficient implicit-explicit BDFk scalar auxiliary variable (SAV) schemes for general dissipative systems. We show that these schemes are unconditionally stable, and lead to a uniform bound of the numerical solution in the norm based on the principal linear operator in the energy. Based on this uniform bound, we carry out a rigorous error analysis for the kth-order (k=1,2,3,4,5) SAV schemes in a unified form for a class of typical Allen-Cahn type and Cahn-Hilliard type equations. We also present numerical results confirming our theoretical convergence rates.

READ FULL TEXT

page 1

page 2

page 3

page 4

03/19/2021

Stability and error analysis of a class of high-order IMEX schemes for Navier-stokes equations with periodic boundary conditions

We construct high-order semi-discrete-in-time and fully discrete (with F...
01/07/2022

The Green's function of the Lax-Wendroff and Beam-Warming schemes

We prove a sharp uniform generalized Gaussian bound for the Green's func...
01/29/2022

A generalized SAV approach with relaxation for dissipative systems

The scalar auxiliary variable (SAV) approach <cit.> and its generalized ...
09/09/2022

Unconditionally energy-stable schemes based on the SAV approach for the inductionless MHD equations

In this paper, we consider numerical approximations for solving the indu...
02/01/2020

The generalized scalar auxiliary variable approach (G-SAV) for gradient flows

We establish a general framework for developing, efficient energy stable...
04/08/2020

Convergence Results for Implicit–Explicit General Linear Methods

This paper studies fixed-step convergence of implicit-explicit general l...
10/07/2019

Explicit and implicit error inhibiting schemes with post-processing

Efficient high order numerical methods for evolving the solution of an o...