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269C, Spring, Vese 

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{\bf Computational Project 2}

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Due on Wednesday, May 31st. 

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Use $P_1$ elements to approximate the solution of 
$$-\triangle u +u=\sin{(2\pi(x+y))},\ (x,y)\in \Omega=\mbox{unit square}$$
with the following boundary conditions: 

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Case (a) $u=0$ for $(x,y)\in \partial \Omega$

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Case (b) $u=0$ for $(x,y)\in \partial \Omega$, $x=0,1$ 

\ \ \ \ \ \ \ \ \ \ \ \ $u_y=0$, for $(x,y)\in \partial \Omega$, $y=0,1$. 

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Base the triangulation on a 10x10 grid. 

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$\bullet$ What you should turn in: the weak formulations, the linear systems, details 
about the discretizations, plots of the results, your computer program, etc. 

$\bullet$ Section 12.2 of the textbook discusses numerical integration 
(quadrature) formulas, helpful to discretize the load vector, if needed.   




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