Abstract
We extend recent results on discrete approximations of the Laplacian in in $\mathbf{R}^d$ with norm resolvent convergence to the corresponding results for Dirichlet and Neumann Laplacians on a half-space. The resolvents of the discrete Dirichlet/Neumann Laplacians are embedded into the continuum using natural discretization and embedding operators. Norm resolvent convergence to their continuous counterparts is proven with a quadratic rate in the mesh size. These results generalize with a limited rate to also include operators with a real, bounded, and Hölder continuous potential, as well as certain functions of the Dirichlet/Neumann Laplacians, including any positive real power.
Originalsprog | Engelsk |
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Tidsskrift | Studia Mathematica |
Vol/bind | 271 |
Nummer | 2 |
Sider (fra-til) | 225-236 |
Antal sider | 12 |
ISSN | 0039-3223 |
DOI | |
Status | Udgivet - 2023 |