An improved error estimate for Maxwell’s equations with a power-law nonlinear conductivity

Convergence analysis of an accurate and efficient method for nonlinear Maxwell's equations

“…By the definition of E 0 h , H 0 h , we get θ 0 E = 0, θ 0 H = 0. Following the same derivation of the error equation (15), we obtain…”

“…Recently, finite element methods have been applied to solve nonlinear Maxwell equation (cf. [5,6,15,18,19]). Numerical schemes with backward Euler discretization in time and mixed conforming finite elements in space were discussed for nonlinear conductivity problems in [5,6].…”

“…A fully-discrete (T, ψ) − ψ e finite element decoupled scheme was developed to solve time-dependent eddy current problem with multipleconnected conductors [2]. Subsequently, an improved convergence rate analysis was presented in [15]. For monotonically increasing conductivity σ(s), the existence of weak solution of system (1a)-(1b) has been proved in [7].…”