Nonconforming Mixed Finite Element Method for Time-dependent Maxwell's Equations with ABC. Issue 2 (24th May 2016)

• Record Type: Journal Article
• Authors: Yao, Changhui; Shi, Dongyang
• Is Part Of: Numerical mathematics. Volume 9:Issue 2(2016)
• Page Start: 193
• Page End: 214
• Publication Date: 2016-05-24
• Subjects: 65N30, -- 65N15, -- 35J25; Maxwell's equations, -- Absorbing boundary condition, -- Nonconforming mixed FEM, -- Semi-discrete and fully discrete schemes; Numerical analysis -- Periodicals; Numerical analysis; Periodicals; 518.05
• DOI: 10.4208/nmtma.2016.m1427
• Languages: English
• ISSNs: 1004-8979

Abstract

Abstract: In this paper, a nonconforming mixed finite element method (FEM) is presented to approximate time-dependent Maxwell's equations in a three-dimensional bounded domain with absorbing boundary conditions (ABC). By employing traditional variational formula, instead of adding penalty terms, we show that the discrete scheme is robust. Meanwhile, with the help of the element's typical properties and derivative transfer skills, the convergence analysis and error estimates for semidiscrete and backward Euler fully-discrete schemes are given, respectively. Numerical tests show the validity of the proposed method.