We present three schemes for the numerical approximation of fractional diffusion, which
build on different definitions of such a non-local process. The first method is a PDE approach …

We review the construction and analysis of numerical methods for strongly nonlinear PDEs,
with an emphasis on convex and non-convex fully nonlinear equations and the convergence …

The term free boundary problem (FBP) refers, in the modern applied mathematical literature,
to a problem in which one or several variables must be determined in different domains of …

We consider a coupled bulk-surface system of partial differential equations with nonlinear
coupling modeling receptor-ligand dynamics. The model arises as a simplification of a …

We obtain regularity results in weighted Sobolev spaces for the solution of the obstacle
problem for the integral fractional Laplacian (− Δ) s in a Lipschitz bounded domain Ω⊂ ℝ n …

We present a posteriori error analysis in the supremum norm for the symmetric interior
penalty discontinuous Galerkin method for the elliptic obstacle problem. We construct …

The purpose of this work is to introduce and analyze a numerical scheme to efficiently solve
boundary value problems involving the spectral fractional Laplacian. The approach is based …

Fractional elliptic quasi-variational inequalities: Theory and numerics Page 1 Interfaces and
Free Boundaries 20 (2018), 1–24 DOI 10.4171/IFB/395 Fractional elliptic quasi-variational …

On a class of nonlocal obstacle type problems related to the distributional Riesz fractional
derivative Page 1 Port. Math. 80 (2023), 157–205 DOI 10.4171/PM/2100 © 2023 Sociedade …

We develop a monotone, two-scale discretization for a class of integrodifferential operators
of order $2 s $, $ s\in (0, 1) $. We apply it to develop numerical schemes, and convergence …