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- Apr 14, 2013

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Hey!!!

Given the following two-point problem:

$$-y''(x)+(by)'(x)=f(x), \forall x \in [0,1]$$

$$y(0)=0, y'(1)=my(1)$$

where $ b \in C^1([0,1];R), f \in C([0,1];R)$ and $ m \in R$ a constant.

Give a finite element method for the construction of the approximation of the solution $y$ of the problem above, where the finite element space ($S$) consists of continuous and partially linear functions.

My idea is the following:

$ u \in S:$

$$ -\int_0^1{u''g}dx+ \int_0^1{bu'g}dx= \int_0^1{fg}dx$$

$$ -u'g|_0^1+ \int_0^1{u'g'}dx+ \int_0^1{bu'g}dx= \int_0^1{fg}dx$$

$$-mu(1)+g(1)+ \int_0^1{u'g'}dx+ \int_0^1{bu'g}dx= \int_0^1{fg}dx$$

$ \forall g \in S$

Could you tell me if this is correct?

Given the following two-point problem:

$$-y''(x)+(by)'(x)=f(x), \forall x \in [0,1]$$

$$y(0)=0, y'(1)=my(1)$$

where $ b \in C^1([0,1];R), f \in C([0,1];R)$ and $ m \in R$ a constant.

Give a finite element method for the construction of the approximation of the solution $y$ of the problem above, where the finite element space ($S$) consists of continuous and partially linear functions.

My idea is the following:

$ u \in S:$

$$ -\int_0^1{u''g}dx+ \int_0^1{bu'g}dx= \int_0^1{fg}dx$$

$$ -u'g|_0^1+ \int_0^1{u'g'}dx+ \int_0^1{bu'g}dx= \int_0^1{fg}dx$$

$$-mu(1)+g(1)+ \int_0^1{u'g'}dx+ \int_0^1{bu'g}dx= \int_0^1{fg}dx$$

$ \forall g \in S$

Could you tell me if this is correct?

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