Exponential integrators for semi-linear parabolic problems with linear constraints

07/05/2019

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by   Robert Altmann, et al.

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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.