Emergent Mind
$Γ$-convergence of Nonlocal Dirichlet Energies With Penalty Formulations of Dirichlet Boundary Data
(2309.10352)
Published Sep 19, 2023
in
math.AP
,
cs.NA
,
and
math.NA
Abstract
We study nonlocal Dirichlet energies associated with a class of nonlocal diffusion models on a bounded domain subject to the conventional local Dirichlet boundary condition. The Dirichlet boundary condition is imposed through a specifically designed penalty formulation. We prove that the nonlocal Dirichlet energies with the penalty terms converge to local Dirichlet energies with Dirichlet boundary conditions in the sense of $\varGamma$-convergence.
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