We found a match
Your institution may have rights to this item. Sign in to continue.
- Title
A Note on a Meshless Method for Fractional Laplacian at Arbitrary Irregular Meshes.
- Authors
García, Ángel; Negreanu, Mihaela; Ureña, Francisco; Vargas, Antonio M.
- Abstract
The existence and uniqueness of the discrete solutions of a porous medium equation with diffusion are demonstrated. The Cauchy problem contains a fractional Laplacian and it is equivalent to the extension formulation in the sense of trace and harmonic extension operators. By using the generalized finite difference method, we obtain the convergence of the numerical solution to the classical/theoretical solution of the equation for nonnegative initial data sufficiently smooth and bounded. This procedure allows us to use meshes with complicated geometry (more realistic) or with an irregular distribution of nodes (providing more accurate solutions where needed). Some numerical results are presented in arbitrary irregular meshes to illustrate the potential of the method.
- Subjects
FINITE difference method; CAUCHY problem; HEAT equation; STATISTICAL smoothing; POROUS materials; FINITE differences
- Publication
Mathematics (2227-7390), 2021, Vol 9, Issue 22, p2843
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math9222843