A new numerical method for div-curl systems with low regularity assumptions. (15th May 2022)

• Record Type: Journal Article
• Authors: Cao, Shuhao; Wang, Chunmei; Wang, Junping
• Is Part Of: Computers & mathematics with applications. Volume 114(2022)
• Page Start: 47
• Page End: 59
• Publication Date: 2022-05-15
• Subjects: Finite element methods -- Weak Galerkin methods -- Primal-dual weak Galerkin -- Div-curl system; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2022.03.015
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: This paper presents a new numerical method for div-curl systems with the normal boundary condition by using a finite element technique known as primal-dual weak Galerkin (PDWG). The PDWG finite element scheme for the div-curl system has two prominent features in that it offers not only an accurate and reliable numerical solution to the div-curl system under the low H α -regularity ( α > 0 ) assumption for the true solution, but also an effective approximation of the normal harmonic vector fields on domains with complex topology. Seven numerical experiments are conducted and the results are presented to demonstrate the performance of the PDWG algorithm, including one example on the computation of discrete normal harmonic vector fields.