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 …

The purpose of this work is to study solution techniques for problems involving fractional
powers of symmetric coercive elliptic operators in a bounded domain with Dirichlet boundary …

We study solution techniques for parabolic equations with fractional diffusion and Caputo
fractional time derivative, the latter being discretized and analyzed in a general Hilbert …

We study solution techniques for a linear-quadratic optimal control problem involving
fractional powers of elliptic operators. These fractional operators can be realized as the …

We design and analyze several finite element methods (FEMs) applied to the Caffarelli–
Silvestre extension that localizes the fractional powers of symmetric, coercive, linear elliptic …

We study a linear-quadratic optimal control problem involving a parabolic equation with
fractional diffusion and Caputo fractional time derivative of orders s∈(0,1) and γ∈(0,1 …

In two-dimensional bounded Lipschitz domains, we analyze a convective Brinkman–
Forchheimer problem on the weighted spaces H 0 1 (ω, Ω)× L 2 (ω, Ω)/R, where ω belongs …

The integral version of the fractional Laplacian on a bounded domain is discretized by a
Galerkin approximation based on piecewise linear functions on a quasiuniform mesh. We …

We develop and analyze multilevel methods for nonuniformly elliptic operators whose
ellipticity holds in a weighted Sobolev space with an $ A_2 $–Muckenhoupt weight. Using …

In this work, we consider the approximation capabilities of shallow neural networks in
weighted Sobolev spaces for functions in the spectral Barron space. The existing literature …