H~1-Galerkin 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, fluid mechanics, boundary layer theory, nonlinear fields and optics. Therefore, the numerical analysis and computing are very mean-ingful.In this article,H1-Galerkin mixed finite element method for one-dimensional parabolic differential equation with singular coefficients are studied. The error estimates in weighted L2-norm and weighted H1-norm for semi-discrete scheme and fully-discrete scheme combined with Euler backward difference scheme are proved.