# Exponential integrators for semi-linear parabolic problems with linear constraints

## TL;DR

This paper develops new exponential integrators for semi-linear parabolic problems with linear constraints, combining existing methods with saddle point solutions to ensure constraints are maintained during time discretization.

## Contribution

It introduces a novel class of semi-explicit exponential integrators that handle constraints effectively, with proven convergence and demonstrated numerical performance.

## Key findings

- Proven convergence rates for the proposed integrators.
- Successful application to parabolic equations with nonlinear boundary conditions.
- Enhanced stability and accuracy in constrained systems.

## 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.