双曲型方程的H1-Galerkin混合有限元法

用H^1-Galerkin混合有限元法解决双曲型方程的初边值问题，此方法与传统的混合元方法相比，不需要验证LBB条件，且两个收敛空间的多项式逼近的次数可以灵活选取，同时也达到了传统混合元相同的收敛阶数．

An H1-Galerkin Mixed Finite Element Methods for Hyperbolic Partial Differential Equation

In this paper,an H^1 -Galerkin mixed finite element method is analyzed for hyperbolic partial differential equations with nonselfadjoint elliptic parts. Compared to the standard H^1-Galerkin procedure, C-continuity for the approximating finite dimensional subspaces can be relaxed for the proposed method. Moreover, it is shown that the finite element approximations have the same rates of convergence as in the calssical mixed method, but without LBB consistency condition and quasiuniformity requirmnent on the finite element metsh. Finally, a better rate of convergence for the flux in L2-norm is derived using modified H^1-Galerkin mixed method in two and three apace dimensions, which confirms the findings in a single space variable and also improves upon the order of convergence of the classical mixed method under extra regularity assumptions of the exact solution.