Finite Element Method

 

1- Implement the fully implicit Fi nite element solution algorithm and use a direct solver (LU factorization) to solve.
2- Plot Error function versus deltaR and DeltaTheta in a log-log scale. Compute the spatial convergence rate.

Sample Solution

proposed bill as an undemocratic power grab. However, for reasons historians still don’t quite understand, shortly after FDR made the plan public, the Court upheld several government regulations it had formerly found unconstitutional. Many have attributed this and similar decisions to a politically motivated change of heart on the part of Justice Owen Roberts. Some legal scholars have rejected this narrative, however, asserting that Roberts’ 1937 decisions were not motivated by Roosevelt’s proposal and can instead be reconciled with his prior jurisprudence. This shifted the majority to favour federal welfare and regulatory enactments. Ultimately by 1942, all but two of the supreme court justices were Roosevelt appointees. Despite the legislative gridlock FDR found himself embroiled in, there was a lot of decisive legislation passed. The creation of the US housing authority provided homes for thousands of Americans. For FDR, more Americans owning more homes meant more consumption, more tax revenue. The Fair Labour Standards Act set employment standards for companies who’s business transcended state boundaries. This meant that corporations had to respect a 40 hour work week, as well as pay a living minimum wage. Perhaps most crucially the act called for the end of child labour. Unfortunately, this only applied to those employed in interstate corporations; domestic servants, agricultural workers, and service employees were not protected. It is only when things start to unfold in Europe that FDR can reconstitute himself as the leader of the people in a time of need.

On the cusp of World War Two FDR runs against and defeats Wendell Wilkie, the Republican nominee for president. This election is key not only due to the events taking place in Europe, but also because of the fact that FDR has now gone against the precedent set by George Washington. Despite heavy campaigning the republicans are unable to dethrone Roosevelt. Roosevelt insisted throughout his campaign that he was only in the race to keep America out of the war in Europe. However, due to the way things unfolded, he would soon be forced to intervene. FDRs third term was dominated by World War Two. Due to the influence of isolationists FDR was unwilling and unable to enter the war immediately. This meant that despite not getting involved in the fighting, the United States would commit to arming and aiding its allies in their fight against the axis powers. Therefore, as Churchill put it, FDR had committed to a policy of “all aid short of war.” In the first of many highly secretive meetings, Roosevelt and Churchill met in August 1941. The outcome of this meeting was the Atlantic Charter, a pivotal piece of conceptual legislature that outlined global wartime and post-war goals. Despite constant pressure from Churchill, FDR did not believe that congress would allow the United States to enter the war. For the time being, the role undertaken by the

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