The Alternating-direction Implicit Characteristic Finite Element Methods for the Three-dimensional Generalized Nerve Conduction Equation (Journal of Partial Differential Equations, 2001)
A complete convergence nnalysis is given for two-level scheme of the alternating-direction implicit characteristic finite element method for the approximate solution of the three-dimensional generalized nerve conduction equation. By use of the calculation of vector product, H^{-1} norm estimates, and a priori estimate theory and technique, the optimal order estimate in L² is obtained.
Keywords: Nerve conduction equation; the alternating-direction implicit; characteristic finite element; optimal order estimate in L²