Problem 2 (55 pts). We now consider the FEM solution of Problem 1. (a) [5pts] Briefly describe the 4 steps necessary to obtain the approximate solution of that BVP using the Galerkin FEM. Use the minimum amount of math necessary to support your explanations. (b) [20pts] Derive the weak form of the BVP. (c) [10pts] Assuming a mesh of two equal elements and linear shape functions, sketch by hand how you expect the FEM solution to look like. Also sketch the analytical solution for comparison. In your sketch, identify the nodal degrees of freedom that the FEM solution seeks to find. (d) [10pts] By analogy with the elastic rod problem and heat conduction problem con- sidered in class, write down the stiffness matrix and force vector for each of the two elements considered in (c). (e) [10pts] Assemble the global system of equations, and verbally explain how to solve it.
Problem 2 (55 pts). We now consider the FEM solution of Problem 1.
(a) [5pts] Briefly describe the 4 steps necessary to obtain the approximate solution of that
BVP using the Galerkin FEM. Use the minimum amount of math necessary to support
your explanations.
(b) [20pts] Derive the weak form of the BVP.
(c) [10pts] Assuming a mesh of two equal elements and linear shape functions, sketch by
hand how you expect the FEM solution to look like. Also sketch the analytical solution
for comparison. In your sketch, identify the nodal degrees of freedom that the FEM
solution seeks to find.
(d) [10pts] By analogy with the elastic rod problem and heat conduction problem considered in class, write down the stiffness matrix and force
elements considered in (c).
(e) [10pts] Assemble the global system of equations, and verbally explain how to solve it.
![Problem 2 (55 pts). We now consider the FEM solution of Problem 1.
(a) [5pts] Briefly describe the 4 steps necessary to obtain the approximate solution of that
BVP using the Galerkin FEM. Use the minimum amount of math necessary to support
your explanations.
(b) [20pts] Derive the weak form of the BVP.
(c) [10pts] Assuming a mesh of two equal elements and linear shape functions, sketch by
hand how you expect the FEM solution to look like. Also sketch the analytical solution
for comparison. In your sketch, identify the nodal degrees of freedom that the FEM
solution seeks to find.
(d) [10pts] By analogy with the elastic rod problem and heat conduction problem con-
sidered in class, write down the stiffness matrix and force vector for each of the two
elements considered in (c).
(e) [10pts] Assemble the global system of equations, and verbally explain how to solve it.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F44771ccb-18ef-4ee9-9657-f17f9fc0e809%2Fe3a31611-a352-4f22-8602-5ea14cf89686%2Fbxszyz_processed.jpeg&w=3840&q=75)
Step by step
Solved in 2 steps with 3 images
