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Abstract

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We introduce a hybrid method to couple continuous Galerkin finite element methods and high-order finite difference methods in a nonconforming multiblock fashion. The aim is to optimize computational efficiency when complex geometries are present. The proposed coupling technique requires minimal changes in the existing schemes while maintaining strict stability, accuracy, and energy conservation. Results are demonstrated on linear and nonlinear scalar conservation laws in two spatial dimensions.

Details

1009240
Subject
Finite element method;
Mathematical analysis;
Galerkin method;
Finite difference method;
Conservation laws;
Coupling
Identifier / keyword
Numerical Analysis
URL
http://arxiv.org/abs/2103.07288
Title
Energy stable and accurate coupling of finite element methods and finite difference methods
Author
Dao, Tuan Anh; Mattsson, Ken; Nazarov, Murtazo
Publication title
arXiv.org; Ithaca
Publication year
2021
Publication date
Apr 7, 2021
Section
Computer Science; Mathematics
Publisher
Cornell University Library, arXiv.org
Source
arXiv.org
Place of publication
Ithaca
Country of publication
United States
University/institution
Cornell University Library arXiv.org
Publication subject
Biology, Statistics, Physics, Mathematics, Engineering--Electrical Engineering, Computers--Computer Engineering, Business And Economics--Banking And Finance
e-ISSN
2331-8422
Source type
Working Paper
Language of publication
English
Document type
Working Paper
Publication history
 
 
Online publication date
2021-11-24
Milestone dates
2021-03-12 (Submission v1); 2021-04-07 (Submission v2)
Publication history
 
 
   First posting date
24 Nov 2021
DOI
https://doi.org/10.1016/j.jcp.2021.110791
ProQuest document ID
2501355919
Document URL
https://www.proquest.com/working-papers/energy-stable-accurate-coupling-finite-element/docview/2501355919/se-2?accountid=208611
Full text outside of ProQuest
http://arxiv.org/abs/2103.07288
Copyright
© 2021. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
Last updated
2021-11-25
Database
ProQuest One Academic