【摘要】 Sobolev方程来源于许多物理过程,在实际中有广泛应用。因此,对该方程提出了许多数值模拟方法,利用H1-Galerkin混合有限元方法分析了线性对流占优Sobolev方程,通过引入Ritz-Volterra投影,利用H lder不等式以及ε-不等式以及三角不等式,得到了未知函数和它的伴随向量函数有限元解的最优阶误差估计,该方法可以使逼近有限元空间Vh和Wh能达成不同次数的多项式空间,与标准混合有限元方法相比,H1-Galerkin混合有限元方法的优点是不需验证LBB相容性条件即可得到和传统混合有限元方法相同的收敛阶数。更多还原

【Abstract】 Sobolev equation is oriented from many physical proceedings,and is widely used in many fields.An H1-Galerkin Mixed Finite Element Method is used to analysise convection-dominated Sobolev equations.By introducing the Ritz-Volterra projection,and using Hlder inequality and ε-inequality and the triangle inequality,optimal error estimates are derived for the finite element solutions of the unknown functions and its gradients in one dimension.This method allows approximation of the finite element space Vh and Wh reach the number of polynomials of different space,thus compared to the standard mixed finite element method,the advantage of the H1-Galerkin method is that approximations solution has the same rate convergence as in the classical mixed finite element methods without the LBB consistency conditions.更多还原