A quadratic finite volume method for nonlinear elliptic problems
type: Item
instance of: scholarly article
title: A quadratic finite volume method for nonlinear elliptic problems
zbMATH Open document ID: 1475.65171
author: Yuanyuan Zhang
author: Chuanjun Chen
author: Chunjia Bi
published in: Advances in Computational Mathematics
publication date: 2021-05-28T00:00:00Z
review text: The authors consider a high order finite volume finite element method to approximate a large class of noninear elliptic equations in two dimensions. The numerical method uses the quadratic finite element spaces on the primal mesh. A nonlinear scheme is established. The existence and uniqueness of the discrete solution is proved. An error estimate of order \(O(h|\ln h|)\) in the \(W^{1,\infty}\)-norm is derived. It is also shown that the discrete solution has an optimal error estimate of order \(O(h^2)\) in the \(H^{1}\)-norm. Some numerical tests are presented to confirm the theoretical results. These error estimates are proved under some suitable assumptions on the exact solution.
reviewed by: Abdallah Bradji
Mathematics Subject Classification ID: 65N08
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35J62
zbMATH DE Number: 7351907
zbMATH Keywords: nonlinear elliptic problems
zbMATH Keywords: higher-order finite volume methods
zbMATH Keywords: error estimates
MaRDI profile type: Publication
full work available at URL: s10444-021-09853-y
OpenAlex ID: W3155604131
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DOI: 10.1007/S10444-021-09853-Y
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description: scientific article; zbMATH DE number 7351907