5 papers · 1 filter
Finite Elements with weighted bases for the fractional Laplacian
Félix del Teso, Stefano Fronzoni, David Gómez-Castro
This work presents a numerical study of the Dirichlet problem for the fractional Laplacian with using Finite Element methods with non-standard bases. Classical…
The Fujita exponent for finite difference approximations of nonlocal and local semilinear blow-up problems
Félix del Teso, Raúl Ferreira
We study monotone finite difference approximations for a broad class of reaction-diffusion problems, incorporating general symmetric Lévy operators. By employing an adaptive time-s…
Numerical methods and regularity properties for viscosity solutions of nonlocal in space and time diffusion equations
Félix del Teso, Łukasz Płociniczak
We consider a general family of nonlocal in space and time diffusion equations with space-time dependent diffusivity and prove convergence of finite difference schemes in the conte…
A finite difference method for the variational -Laplacian
Félix del Teso, Erik Lindgren
We propose a new monotone finite difference discretization for the variational -Laplace operator, \[ Δ_p u=\text{div}(|\nabla u|^{p-2}\nabla u), \] and present a convergent nume…
Numerical approximations for fractional elliptic equations via the method of semigroups
Nicole Cusimano, Félix del Teso, Luca Gerardo-Giorda
We provide a novel approach to the numerical solution of the family of nonlocal elliptic equations in , subject to some homogeneous boundary conditions $\mathcal{B}(…