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

Abstract

We construct efficient implicit-explicit BDF$k$ 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 $k$th-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.

References in corpus (1)

• The BDF3/EP3 scheme for MBE with no slope selection is stable

Cited by in corpus (4)

• A generalized SAV approach with relaxation for dissipative systems
• Stability and convergence of relaxed scalar auxiliary variable schemes for Cahn-Hilliard systems with bounded mass source
• Scalar auxiliary variable (SAV) stabilization of implicit-explicit (IMEX) time integration schemes for nonlinear structural dynamics
• Energy dissipation law and maximum bound principle-preserving linear BDF2 schemes with variable steps for the Allen-Cahn equation