Two-grid FEM for fractional diffusion problems with limited regularity

Abstract

This paper presents a two-grid finite element method for solving semilinear fractional evolution equations on bounded convex domains. In contrast to existing studies that assume strong regularity for the exact solution, our approach rigorously addresses the limited smoothing properties of the fractional model. Through a combination of semigroup theory and energy estimates, we derive optimal error bounds under low regularity assumptions. The method achieves fine-grid accuracy while significantly reducing computational costs. Numerical experiments validate the theoretical convergence rates and demonstrate the effectiveness of the two-grid approach for fractional diffusion problems.