Unconditional Optimal Error Estimates of BDF-Galerkin FEMs for Nonlinear Thermistor Equations

In this paper we study linearized backward differential formula (BDF) type schemes with Galerkin finite element approximations for the time-dependent nonlinear thermistor equations. Optimal L2 error estimates for the proposed schemes are proved unconditionally. The proof consists of two steps. First, the boundedness of the numerical solution in certain strong norms is obtained by a temporal-spatial error splitting argument. Second, a traditional approach is used to provide an optimal L2 error estimate for r-th order FEMs (r ≥ 1). Numerical experiments in both two and three dimensional spaces are conducted to confirm our theoretical analysis and show the high order accuracy and unconditional stability (convergence) of the linearized BDF–Galerkin FEMs. Keywords Nonlinear parabolic system · Unconditional convergence · Optimal error estimates · Linearized semi-implicit scheme · BDF scheme · Galerkin method Mathematics Subject Classification 65M12 · 65N30 · 35K61

• Type: Journal
• Year: 2016
• Where: JSCIC
• Authors: Huadong Gao
• Keywords: JSCIC 2016