Exponential integrators for semi-linear parabolic problems with linear constraints

2019/07/05 by Altmann, Robert, Zimmer, Christoph
#65J15 #65L80 #65M12 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1907.02828

Abstract

This paper is devoted to the construction of exponential integrators of first and second order for the time discretization of constrained parabolic systems. For this extend, we combine well-known exponential integrators for unconstrained systems with the solution of certain saddle point problems in order to meet the constraints throughout the integration process. The result is a novel class of semi-explicit time integration schemes. We prove the expected convergence rates and illustrate the performance on two numerical examples including a parabolic equation with nonlinear dynamic boundary conditions.

Related

• Exponential integrators for parabolic problems with non-homogeneous boundary conditions
• Low regularity integrators for semilinear parabolic equations with maximum bound principles
• An exponential Integrator for finite volume discretization of nonlinear parabolic differential equation
• A high-order exponential integrator for nonlinear parabolic equations with nonsmooth initial data
• On the implementation of exponential methods for semilinear parabolic equations