请问什么能用拉格朗日插值函数构造的形函数

吃河蟹的稻草人

我在书上看到 C0阶连续问题可以应用拉格朗日插值，那么C0，C0阶是指二阶微分方程或者弹性力学问题，谁能具体说下什么样的问题可以用拉格朗日法，这个2阶方程是属于什么的方程，还有它的缺点是占用很多内节点，这是什么问题？？

tonnyw

1# 吃河蟹的稻草人

Finite element has different kinds of shape functions. Lagrange interpolation is just one of them. I don't understand what you mean by C0.

For elliptic problem, such as heat conduction and elasticity, the governing equation is second order in derivative which requires the solution has to be C1, namely, the solution has to have continuous first order derivative. If we look at the weak form of the governing equation, we can see that we just need the finite element solution to be C0 function and its first order derivative is square integrable which makes sure the energy finite. You can see the requirement for the continuity of derivative is lowered. That's why we call it weak form.

If the governing equation is fourth order, such as for shell, beam, and plate where the equation is biharmonic, then the shape function has to be C1 function and its second order derivative has to be square integrable.

refeihc

呵呵，这样的问题会把人问得吐血。

建议你提问话要说完整。

我猜第一句是想说：“任何C0阶连续函数可以应用拉格朗日插值多项式来逼近，多项式的阶次越高，逼近精度也就越高”。

不知我猜得对不对？

refeihc

再猜第二句“那么C0，C0阶是指二阶微分方程或者弹性力学问题”

是不是想说：“二阶微分方程或弹性力学问题的解在边界上要满足C0阶光滑条件”？

不知后面能不能猜出来，先猜再想办法回答，呵呵，好玩。

吃河蟹的稻草人

你好 可以告诉QQ吗，方便的话直接在Q上和你说 谢谢

refeihc

2楼所说的热传导方程应该是抛物型的吧

refeihc

回楼主，我不用QQ的，就在这里交流吧，你注意表达清楚就是了。

si13

ls的签名档不是很赞同

ql2120

“C0阶是指二阶微分方程或者弹性力学问题”？   楼主是在哪里看到的？