22 citations · 67 across the 16 of their papers we have counts for
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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 \…
Robust numerical methods for nonlocal (and local) equations of porous medium type. Part II: Schemes and experiments
Félix del Teso, Jørgen Endal, Espen R. Jakobsen
We develop unified and easy to use framework to study robust fully discrete numerical methods for nonlinear degenerate diffusion equations $$ \partial_t u-\mathfrak{L}[φ(u)]=f(x,t)…
Robust numerical methods for nonlocal (and local) equations of porous medium type. Part I: Theory
Félix del Teso, Jørgen Endal, Espen R. Jakobsen
We develop a unified and easy to use framework to study robust fully discrete numerical methods for nonlinear degenerate diffusion equations $$ \partial_t u-\mathfrak{L}^{σ,μ}[φ(u)…
Discretizations of the spectral fractional Laplacian on general domains with Dirichlet, Neumann, and Robin boundary conditions
Nicole Cusimano, Félix del Teso, Luca Gerardo-Giorda +1
In this work, we propose novel discretizations of the spectral fractional Laplacian on bounded domains based on the integral formulation of the operator via the heat-semigroup form…
Finite difference method for a general fractional porous medium equation
Félix del Teso, Juan Luis Vázquez
We formulate a numerical method to solve the porous medium type equation with fractional diffusion \[ \frac{\partial u}{\partial t}+(-Δ)^{σ/2} (u^m)=0 \] posed for $x\in \mathbb{R}…