Question: 1. Solve the boundary value problem y+x=0 with boundary conditions y(0)= 0 and y(1.5)=1 by hand using Galerkin finite elements method and isoparametric shape functions
1. Solve the boundary value problem y+x=0 with boundary conditions y(0)= 0 and y(1.5)=1 by hand using Galerkin finite elements method and isoparametric shape functions (see example in Lectures 17 and 18). Use three elements of equal length hi=0.5 each. Clearly denote solution steps 1-9 in your submission. You can use Matlab or any other software to evaluate the integrals and solve the resulting system of equations. 2. Solve the same boundary value problem by hand using the Finite Differences method. Use three segments of equal length hi=0.5 each. Compare the results. (Hint: Variable x can be expressed in the isoparametric coordinate system as x=NL(t)xi+NR(t)xi+1, where xi and xi+1 are the coordinates of the nodes of element \#i)
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