Numerical methods for nonlocal and fractional models

M D'Elia, Q Du, C Glusa, M Gunzburger, X Tian… - Acta Numerica, 2020 - cambridge.org
Partial differential equations (PDEs) are used with huge success to model phenomena
across all scientific and engineering disciplines. However, across an equally wide swath …

Optimal operator preconditioning for pseudodifferential boundary problems

H Gimperlein, J Stocek, C Urzúa-Torres - Numerische Mathematik, 2021 - Springer
We propose an operator preconditioner for general elliptic pseudodifferential equations in a
domain\varOmega Ω, where\varOmega Ω is either in R^ n R n or in a Riemannian manifold …

Linear and nonlinear fractional elliptic problems

JP Borthagaray, W Li, RH Nochetto - 75 years of mathematics of …, 2020 - books.google.com
This paper surveys recent analytical and numerical research on linear problems for the
integral fractional Laplacian, fractional obstacle problems, and fractional minimal graphs …

[PDF][PDF] Linear and nonlinear fractional diffusion

JP Borthagaray, W Li, RH Nochetto - arXiv preprint arXiv …, 2019 - researchgate.net
This paper surveys recent analytical and numerical research on linear problems for the
integral fractional Laplacian, fractional obstacle problems, and fractional minimal graphs …