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University of Michigan vía Coursera
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The Finite Element Method for Problems in Physics

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  • 1
    • This unit is an introduction to a simple one-dimensional problem that can be solved by the finite element method.
  • 2
    • In this unit you will be introduced to the approximate, or finite-dimensional, weak form for the one-dimensional problem.
  • 3
    • In this unit, you will write the finite-dimensional weak form in a matrix-vector form. You also will be introduced to coding in the deal.ii framework.
  • 4
    • This unit develops further details on boundary conditions, higher-order basis functions, and numerical quadrature. You also will learn about the templates for the first coding assignment.
  • 5
    • This unit outlines the mathematical analysis of the finite element method.
  • 6
    • This unit develops an alternate derivation of the weak form, which is applicable to certain physical problems.
  • 7
    • In this unit, we develop the finite element method for three-dimensional scalar problems, such as the heat conduction or mass diffusion problems.
  • 8
    • In this unit, you will complete some details of the three-dimensional formulation that depend on the choice of basis functions, as well as be introduced to the second coding assignment.
  • 9
    • In this unit, we take a detour to study the two-dimensional formulation for scalar problems, such as the steady state heat or diffusion equations.
  • 10
    • This unit introduces the problem of three-dimensional, linearized elasticity at steady state, and also develops the finite element method for this problem. Aspects of the code templates are also examined.
  • 11
    • In this unit, we study the unsteady heat conduction, or mass diffusion, problem, as well as its finite element formulation.
  • 12
    • In this unit we study the problem of elastodynamics, and its finite element formulation.
  • 13
    • This is a wrap-up, with suggestions for future study.