Nonsmooth data error estimates for exponential Runge-Kutta methods and applications to split exponential integrators
By: Qiumei Huang, Alexander Ostermann, Gangfan Zhong
Potential Business Impact:
Makes computer models of heat and fluid flow accurate.
We derive error bounds for exponential Runge-Kutta discretizations of parabolic equations with nonsmooth initial data. Our analysis is carried out in a framework of abstract semilinear evolution equations with operators having non-dense domain. In particular, we investigate nonsmooth data error estimates for the Allen-Cahn and the Burgers' equation. As an application, we apply these nonsmooth data error estimates to split exponential integrators and derive a convergence result in terms of the data.
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