A mass conservative characteristic finite element method with unconditional optimal convergence for semiconductor device problem

Abstract

We consider a mass conservative type method for semiconductor device problem by employing mixed finite element method (FEM) for electric potential equation and mass conservative characteristic FEM for both electron and hole density equations. The boundedness of numerical solution without certain time‐step restriction and optimal error estimates of full discrete scheme are proved. Numerical experiment is presented to verify the effectiveness and unconditional stability of the proposed method.