RT Journal Article
T1 A Note on a Meshless Method for Fractional Laplacian at Arbitrary Irregular Meshes
A1 García, Ángel
A1 Negreanu Pruna, Mihaela
A1 Ureña, Francisco
A1 Vargas, Antonio M.
AB 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.
SN 2227-7390
YR 2021
FD 2021
LK https://hdl.handle.net/20.500.14352/7344
UL https://hdl.handle.net/20.500.14352/7344
LA eng
NO Este artículo pertenece a un número especial de Applications of Partial Differential Equations in Engineering
DS Docta Complutense
RD 31 dic 2025