Mixed Finite Element Methods For One-dimensional Singular Differential Equation

The differential equations with singular coefficients are very important ones in practical problems, such as nuclear physics, gas dynamics, mochanics, boundary layer theory, nonlin-ear fields and optics. Therefore, the numerical analysis and computing are very meaningful. The traditional finite difference and finite element methods for elliptic and parabolic dif-ferential equations with singular coefficients have been studied extensively and some ideal results have been obtained.In this article, mixed finite element method for two-point boundary value problem and one-dimensional parabolic differential equation with singular coefficients are studied for the first time. The error estimates in weighted L2-norm for semi-discrete scheme and fully-discrete scheme combined with Euler backward difference scheme are proved.