Consider the following strong form. d'u -u+z=0 for 0...

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Consider the following strong form. d'u -u+z=0 for 0<x<1. u(0)=0 (1) 0 Construct a Ritz-Galerkin finite element solution for the problem using the following roadmap. (a) Discretize the domain into 3 equal length elements. (b) Construct the weak form for the problem over the domain of a generic two-noded element with end nodes i and j. Assume coordinates of the two end nodes are r, and r,. Identify the primary variable and the secondary variable from the boundary terms in the weak form. Replace the secondary variables in the boundary terms of the weak form by assumed values of P, and P, at the boundary nodes i and j, respectively. Using a Co linear interpolation for the element, obtain the stiffness matrix and the force vector for-the linear element. Expressions in the stiffness matrix and force vector will be in terms of z, and rj. dr2 (c) For each of the three elements in the problem, compute the element stiffness matrix and force vector using the expressions obtained from the previous step. Assemble the element stiffness matrices and force vectors into the global stiffness matrix and force vector. (d) Apply the boundary conditions and obtain a reduced system of equations. (e) Solve the reduced system to obtain the values of the primary variable at all nodes. (f) Construct a plot of the primary variable as a function of position over the domain of the problem. Consider the following strong form. d'u -u+z=0 for 0<x<1. u(0)=0 (1) 0 Construct a Ritz-Galerkin finite element solution for the problem using the following roadmap. (a) Discretize the domain into 3 equal length elements. (b) Construct the weak form for the problem over the domain of a generic two-noded element with end nodes i and j. Assume coordinates of the two end nodes are r, and r,. Identify the primary variable and the secondary variable from the boundary terms in the weak form. Replace the secondary variables in the boundary terms of the weak form by assumed values of P, and P, at the boundary nodes i and j, respectively. Using a Co linear interpolation for the element, obtain the stiffness matrix and the force vector for-the linear element. Expressions in the stiffness matrix and force vector will be in terms of z, and rj. dr2 (c) For each of the three elements in the problem, compute the element stiffness matrix and force vector using the expressions obtained from the previous step. Assemble the element stiffness matrices and force vectors into the global stiffness matrix and force vector. (d) Apply the boundary conditions and obtain a reduced system of equations. (e) Solve the reduced system to obtain the values of the primary variable at all nodes. (f) Construct a plot of the primary variable as a function of position over the domain of the problem. Consider the following strong form. d'u -u+z=0 for 0<x<1. u(0)=0 (1) 0 Construct a Ritz-Galerkin finite element solution for the problem using the following roadmap. (a) Discretize the domain into 3 equal length elements. (b) Construct the weak form for the problem over the domain of a generic two-noded element with end nodes i and j. Assume coordinates of the two end nodes are r, and r,. Identify the primary variable and the secondary variable from the boundary terms in the weak form. Replace the secondary variables in the boundary terms of the weak form by assumed values of P, and P, at the boundary nodes i and j, respectively. Using a Co linear interpolation for the element, obtain the stiffness matrix and the force vector for-the linear element. Expressions in the stiffness matrix and force vector will be in terms of z, and rj. dr2 (c) For each of the three elements in the problem, compute the element stiffness matrix and force vector using the expressions obtained from the previous step. Assemble the element stiffness matrices and force vectors into the global stiffness matrix and force vector. (d) Apply the boundary conditions and obtain a reduced system of equations. (e) Solve the reduced system to obtain the values of the primary variable at all nodes. (f) Construct a plot of the primary variable as a function of position over the domain of the problem. Consider the following strong form. d'u -u+z=0 for 0<x<1. u(0)=0 (1) 0 Construct a Ritz-Galerkin finite element solution for the problem using the following roadmap. (a) Discretize the domain into 3 equal length elements. (b) Construct the weak form for the problem over the domain of a generic two-noded element with end nodes i and j. Assume coordinates of the two end nodes are r, and r,. Identify the primary variable and the secondary variable from the boundary terms in the weak form. Replace the secondary variables in the boundary terms of the weak form by assumed values of P, and P, at the boundary nodes i and j, respectively. Using a Co linear interpolation for the element, obtain the stiffness matrix and the force vector for-the linear element. Expressions in the stiffness matrix and force vector will be in terms of z, and rj. dr2 (c) For each of the three elements in the problem, compute the element stiffness matrix and force vector using the expressions obtained from the previous step. Assemble the element stiffness matrices and force vectors into the global stiffness matrix and force vector. (d) Apply the boundary conditions and obtain a reduced system of equations. (e) Solve the reduced system to obtain the values of the primary variable at all nodes. (f) Construct a plot of the primary variable as a function of position over the domain of the problem.

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To construct a RitzGalerkin finite element solution for the given problem lets follow the roadmap provided a Discretize the domain into 3 equallength ... View the full answer