Consider the weak form of the one-dimensional Laplace equation [ kw udQ + [ wf dN...

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Consider the weak form of the one-dimensional Laplace equation [₂ kw udQ + [ wf dN + w(0)ā = 0, = where Ω (0, 1) and k> 0 is a constant. Assume that the admissible fields U and W for u and w, respectively, allow the first derivative of u and w to exhibit finite jumps at points with = in, i=1.2.....n, and show that n pli+1 Σ w(ku,rr i=0 JX₂ TO X - 1 f) d + w(0) [kur (0) + Σw(x;)k[u,x(x†) — U‚¸x(x7)] = 0. TL i=1 From the above equation derive the strong form of the problem. What can you conclude regarding smoothness of the exact solution across the points with x = x₂? - q] In Xn+1 u(1) = U Consider the weak form of the one-dimensional Laplace equation [₂ kw udQ + [ wf dN + w(0)ā = 0, = where Ω (0, 1) and k> 0 is a constant. Assume that the admissible fields U and W for u and w, respectively, allow the first derivative of u and w to exhibit finite jumps at points with = in, i=1.2.....n, and show that n pli+1 Σ w(ku,rr i=0 JX₂ TO X - 1 f) d + w(0) [kur (0) + Σw(x;)k[u,x(x†) — U‚¸x(x7)] = 0. TL i=1 From the above equation derive the strong form of the problem. What can you conclude regarding smoothness of the exact solution across the points with x = x₂? - q] In Xn+1 u(1) = U

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ANSWER To show the given equation we can start by integrating the weak form by parts int Omega kw x ... View the full answer