A Note on a Meshless Method for Fractional Laplacian at Arbitrary Irregular Meshes

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 fi...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Ángel García, Mihaela Negreanu, Francisco Ureña, Antonio M. Vargas
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	fractional Laplacian generalized finite difference method discrete maximum principle convergence Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/647122859e5a44fea10f14b86b3ca2d7
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:doaj.org-article:647122859e5a44fea10f14b86b3ca2d7
record_format	dspace
spelling	oai:doaj.org-article:647122859e5a44fea10f14b86b3ca2d72021-11-25T18:16:28ZA Note on a Meshless Method for Fractional Laplacian at Arbitrary Irregular Meshes10.3390/math92228432227-7390https://doaj.org/article/647122859e5a44fea10f14b86b3ca2d72021-11-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/22/2843https://doaj.org/toc/2227-7390The 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.Ángel GarcíaMihaela NegreanuFrancisco UreñaAntonio M. VargasMDPI AGarticlefractional Laplaciangeneralized finite difference methoddiscrete maximum principleconvergenceMathematicsQA1-939ENMathematics, Vol 9, Iss 2843, p 2843 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	fractional Laplacian generalized finite difference method discrete maximum principle convergence Mathematics QA1-939
spellingShingle	fractional Laplacian generalized finite difference method discrete maximum principle convergence Mathematics QA1-939 Ángel García Mihaela Negreanu Francisco Ureña Antonio M. Vargas A Note on a Meshless Method for Fractional Laplacian at Arbitrary Irregular Meshes
description	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.
format	article
author	Ángel García Mihaela Negreanu Francisco Ureña Antonio M. Vargas
author_facet	Ángel García Mihaela Negreanu Francisco Ureña Antonio M. Vargas
author_sort	Ángel García
title	A Note on a Meshless Method for Fractional Laplacian at Arbitrary Irregular Meshes
title_short	A Note on a Meshless Method for Fractional Laplacian at Arbitrary Irregular Meshes
title_full	A Note on a Meshless Method for Fractional Laplacian at Arbitrary Irregular Meshes
title_fullStr	A Note on a Meshless Method for Fractional Laplacian at Arbitrary Irregular Meshes
title_full_unstemmed	A Note on a Meshless Method for Fractional Laplacian at Arbitrary Irregular Meshes
title_sort	note on a meshless method for fractional laplacian at arbitrary irregular meshes
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/647122859e5a44fea10f14b86b3ca2d7
work_keys_str_mv	AT angelgarcia anoteonameshlessmethodforfractionallaplacianatarbitraryirregularmeshes AT mihaelanegreanu anoteonameshlessmethodforfractionallaplacianatarbitraryirregularmeshes AT franciscourena anoteonameshlessmethodforfractionallaplacianatarbitraryirregularmeshes AT antoniomvargas anoteonameshlessmethodforfractionallaplacianatarbitraryirregularmeshes AT angelgarcia noteonameshlessmethodforfractionallaplacianatarbitraryirregularmeshes AT mihaelanegreanu noteonameshlessmethodforfractionallaplacianatarbitraryirregularmeshes AT franciscourena noteonameshlessmethodforfractionallaplacianatarbitraryirregularmeshes AT antoniomvargas noteonameshlessmethodforfractionallaplacianatarbitraryirregularmeshes
_version_	1718411385111576576

A Note on a Meshless Method for Fractional Laplacian at Arbitrary Irregular Meshes

Ejemplares similares