Tuesday, March 18, 2025 - 09:00 in V2-205
A monotone discretization for integral fractional Laplacian on bounded Lipschitz domains
A talk in the Nonlocal Equations: Analysis and Numerics series by
Shuonan Wu from Beijing
| Abstract: |
We propose a monotone discretization method for the integral fractional
Laplacian on bounded Lipschitz domains with homogeneous Dirichlet boundary conditions, specifically designed for solving fractional obstacle problems. Operating on unstructured grids in arbitrary dimensions, the method
offers flexibility in approximating singular integrals over a domain that depends not only on the local grid size but also on the distance to the
boundary, where the Hölder regularity of the solution deteriorates. Using a discrete barrier function reflecting this distance, we establish optimal
pointwise convergence rates in terms of the Hölder regularity of the data
on both quasi-uniform and graded grids. The method can be directly applied to fractional obstacle problems, and an improved policy iteration is
proposed to achieve better numerical performance.
Within the CRC this talk is associated to the project(s): A7 |
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