Tuesday, March 18, 2025 - 09:40 in V2-205
Local discontinuous Galerkin methods for the integral fractional Laplacian
A talk in the Nonlocal Equations: Analysis and Numerics series by
Rubing Han from Beijing
| Abstract: |
We propose local discontinuous Galerkin (LDG) and minimal dissipation
LDG (md-LDG) methods for solving the integral fractional Laplacian problem. Using the Riesz potential, we reformulate the problem in a 3-field
mixed form. By the error equation, we establish a priori error estimates for
the LDG scheme on polygonal meshes. For triangular meshes, we prove
better a priori error estimates for both LDG and md-LDG schemes by utilizing continuous interpolation and special projection. Combining with the
regularity theories, we demonstrate the convergence rates of these schemes
on both quasi-uniform and graded meshes. Numerical experiments are provided to validate the effectiveness of our theoretical results
Within the CRC this talk is associated to the project(s): A7 |
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