A conforming discontinuous Galerkin finite element method on rectangular partitions
type: Item
instance of: scholarly article
title: A conforming discontinuous Galerkin finite element method on rectangular partitions
zbMATH Open document ID: 1478.65122
author: Yue Feng
author: Ruishu Wang
author: Shangyou Zhang
author: Yu Jie Liu
published in: Electronic Research Archive
publication date: 2021-06-07T00:00:00Z
review text: This paper presents a new conforming discontinuous Galerkin (DG) scheme for second order elliptic equations on rectangular partitions. The new method is based on DG finite element space and uses a weak gradient arising from local Raviart-Thomas space for gradient approximations. By using the weak gradient and enforcing inter-element continuity strongly, the scheme maintains the simple formulation of conforming finite element method while have the flexibility of using discontinuous approximations. Hence, the programming complexity of this new conforming DG scheme is reduced compared to other existing DG methods. Error estimates of optimal order are established for the corresponding conforming DG approximations in energy norm and \(L^2\)-norm. Numerical results are presented to confirm the theoretical rates of convergence.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35J50
Mathematics Subject Classification ID: 35J15
zbMATH DE Number: 7355954
zbMATH Keywords: conforming discontinuous Galerkin finite element method
zbMATH Keywords: second order elliptic problem
zbMATH Keywords: rectangular partitions
zbMATH Keywords: error estimates
reviewed by: Vit Dolejsi
MaRDI profile type: Publication
full work available at URL: era.2020120
OpenAlex ID: W3108878348
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DOI: 10.3934/ERA.2020120
description: scientific article; zbMATH DE number 7355954