Nonlocal Venttsel' diffusion in fractal-type domains: regularity results and numerical approximation

Massimo Cefalo; Simone Creo; Maria Rosaria Lancia; Paola Vernole

doi:10.1002/mma.5686

Nonlocal Venttsel' diffusion in fractal-type domains: regularity results and numerical approximation

Massimo Cefalo
, Simone Creo
, Maria Rosaria Lancia
, Paola Vernole

University of Rome La Sapienza

Research output: Contribution to journal › Article › peer-review

Abstract

We study a nonlocal Venttsel' problem in a nonconvex bounded domain with a Koch-type boundary. Regularity results of the strict solution are proved in weighted Sobolev spaces. The numerical approximation of the problem is carried out, and optimal a priori error estimates are obtained.

Original language	English
Pages (from-to)	4712-4733
Number of pages	22
Journal	Mathematical Methods in the Applied Sciences
Volume	42
Issue number	14
Early online date	5 Jun 2019
DOIs	https://doi.org/10.1002/mma.5686
Publication status	Published - 30 Sept 2019
Externally published	Yes

Keywords

finite element method
Koch snowflake domain
nonlocal problems
numerical approximation
regularity results
Venttsel' boundary conditions
weighted Sobolev spaces

Access to Document

10.1002/mma.5686Licence: Other

Cite this

@article{9355e2d63be0462fa15a12bf70973e8f,

title = "Nonlocal Venttsel' diffusion in fractal-type domains: regularity results and numerical approximation",

abstract = "We study a nonlocal Venttsel' problem in a nonconvex bounded domain with a Koch-type boundary. Regularity results of the strict solution are proved in weighted Sobolev spaces. The numerical approximation of the problem is carried out, and optimal a priori error estimates are obtained.",

keywords = "finite element method, Koch snowflake domain, nonlocal problems, numerical approximation, regularity results, Venttsel' boundary conditions, weighted Sobolev spaces",

author = "Massimo Cefalo and Simone Creo and Lancia, \{Maria Rosaria\} and Paola Vernole",

year = "2019",

month = sep,

day = "30",

doi = "10.1002/mma.5686",

language = "English",

volume = "42",

pages = "4712--4733",

journal = "Mathematical Methods in the Applied Sciences",

issn = "0170-4214",

publisher = "John Wiley and Sons Ltd",

number = "14",

}

TY - JOUR

T1 - Nonlocal Venttsel' diffusion in fractal-type domains

T2 - regularity results and numerical approximation

AU - Cefalo, Massimo

AU - Creo, Simone

AU - Lancia, Maria Rosaria

AU - Vernole, Paola

PY - 2019/9/30

Y1 - 2019/9/30

N2 - We study a nonlocal Venttsel' problem in a nonconvex bounded domain with a Koch-type boundary. Regularity results of the strict solution are proved in weighted Sobolev spaces. The numerical approximation of the problem is carried out, and optimal a priori error estimates are obtained.

AB - We study a nonlocal Venttsel' problem in a nonconvex bounded domain with a Koch-type boundary. Regularity results of the strict solution are proved in weighted Sobolev spaces. The numerical approximation of the problem is carried out, and optimal a priori error estimates are obtained.

KW - finite element method

KW - Koch snowflake domain

KW - nonlocal problems

KW - numerical approximation

KW - regularity results

KW - Venttsel' boundary conditions

KW - weighted Sobolev spaces

U2 - 10.1002/mma.5686

DO - 10.1002/mma.5686

M3 - Article

AN - SCOPUS:85067379646

SN - 0170-4214

VL - 42

SP - 4712

EP - 4733

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

IS - 14

ER -

Nonlocal Venttsel' diffusion in fractal-type domains: regularity results and numerical approximation

Abstract

Keywords

Access to Document

Fingerprint

Cite this