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arXiv · 2511.18180

Space-time adaptive methods for parabolic evolution equations

Jun Wang·Jie Su·Leslie Greengard·Shidong Jiang·Shravan Veerapaneni
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Abstract

We present a family of integral equation-based solvers for the heat equation, reaction-diffusion systems, the unsteady Stokes equation and the incompressible Navier-Stokes equations in two space dimensions. Our emphasis is on the development of methods that can efficiently follow complex solution features in space-time by refinement and coarsening at each time step on an adaptive quadtree. For simplicity, we focus on problems posed in a square domain with periodic boundary conditions. The performance and robustness of the methods are illustrated with several numerical examples.

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Jun Wang, Jie Su, Leslie Greengard, Shidong Jiang, Shravan Veerapaneni. 2025-11-22. Space-time adaptive methods for parabolic evolution equations. https://arxiv.org/abs/2511.18180

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