Domain decomposition methods: Difference between revisions

Revision as of 05:36, 1 November 2019

Revision as of 18:58, 15 February 2020

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The exact solution is:<br>

<math> u(x)=\frac{e^x-e^{-x}}{e^{1}-e^{-1}} </math><br>

Subdivide the ___domain into two subdomains, one from <math>\left[0,\frac{1}{2}\right]</math> and another from <math>\left[\frac{1}{2},1\right]</math>. In eachthe ofleft these two subdomainssubdomain define the interpolating functionsfunction <math> v_1(x) </math> and in the right define <math> v_2 (x) </math>. At the interface between these two subdomains the following interface conditions shall be imposed:<br>

<math> v_1\left(\frac{1}{2}\right)=v_2 \left(\frac{1}{2}\right) </math><br>

<math> v_1'\left(\frac{1}{2}\right)=v_2'\left(\frac{1}{2}\right)</math><br>