6 papers
A Viscosity Framework for Dynamic Programming Principles and Applications
Félix del Teso, Julio D. Rossi, Jorge Ruiz-Cases
In this work we introduce a viscosity-based notion of solution for general approximation schemes associated with partial differential equations, such as dynamic programming princip…
A convergent finite difference-quadrature scheme for the porous medium equation with nonlocal pressure
Félix del Teso, Espen R. Jakobsen
We introduce and analyze a numerical approximation of the porous medium equation with fractional potential pressure introduced by Caffarelli and Vázquez: \[ \partial_t u = \nabla…
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. Classica…
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-…
Game theoretical asymptotic mean value properties for non-homogeneous -Laplace problems
Félix del Teso, Julio D. Rossi
We extend the classical mean value property for the Laplacian operator to address a nonlinear and non-homogeneous problem related to the -Laplacian operator for . Specifica…
A note on the L1 discretization error for the Caputo derivative in Hölder spaces
Félix del Teso, Åukasz PÅociniczak
We establish uniform error bounds of the L1 discretization of the Caputo derivative of Hölder continuous functions. The result can be understood as: error = (degree of smoothness…