The existence and uniqueness of the solution to these problems with the use of FEM are proved and optimal error estimates in weighted L2-norm are given.

本文讨论二维奇异非稳态问题的有限元方法，证明了弱解的存在唯一性，并给出有限元解的加权L2-模估计。

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Then based on it, we give an estimation on the difference between this local entropy solution and the solution of the quasi-one-dimensional problem in L2 norm.

然后在此基础上，我们讨论了上述熵解同拟一维流问题的解在L2意义下的相近程度。

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Then based on it, we give an estimation on the difference between this local entropy solution and the solution of the quasi-one-dimensional problem in L2 norm.

然后在此基础上，我们讨论了上述熵解同拟一维流问题的解在L2意义下的相近程度。

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