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1

In this course, we will discuss the strong form of steady-state heat conduction and mass diffusion. We will introduce Fourier's law of heat conduction and temperature, and heat flux will also be discussed, as well as boundary conditions like ...Read more

2

This course was developed by Prof. Krishna Garikipati and Dr. Gregory Teichert, at the University of Michigan in partnership with Ansys. In this course, we begin by discussing linear elliptic partial differential equations (PDEs) in one dimension. We discuss vari...Read more

3

In this course, we discuss how the infinite-dimensional weak form of a 1D linear elliptic partial differential equation (PDE) can be transformed to a finite-dimensional weak form, which forms the basis of the finite element method. We discuss basic Hilbert spa...Read more

4

In this course, we derive the matrix-vector weak form, which is used in the finite element method. We begin by deriving the matrix-vector form for a single general element, then proceed to derive it for the entire problem domain by assembling the matrix-vector forms for...Read more

5

We begin this course with a discussion about boundary conditions. We discuss a pure Dirichlet problem using an example of a linear elastic bar. We then move on to developing higher-order polynomial basis functions for Lagrange polynomials and discuss some properties of Lag...Read more

6

This course discusses why and how finite element analysis (FEA) works and the special properties of FEA. The norms that represent the finite-dimensional trial solution will be discussed. The important properties of the finite element method consistency and th...Read more

7

This course focuses on obtaining the weak form using variational methods. Further, it discusses potential energy, or Gibbs free energy. We will talk about ‘pi’ as free energy functional and how the extrema can be used to check equilibrium states. Next, we discuss the variation in ‘pi’ with ...Read more

8

In this course, we will discuss the use of Lagrange polynomials in the basis functions in 1D through 3D. The formula for the basis functions is first written in 2D, then in 3D. We will further talk about the Gaussian quad...Read more

9

This course discusses the process of building two-dimensional problems for the linear and elliptic PDEs using a scalar variable. The strong and the weak form are discussed using constitutive relations a...Read more

10

This course was developed by Prof. Krishna Garikipati and Dr. Gregory Teichert, at the University of Michigan in partnership with Ansys. In this course, we will derive the finite element equations for linear elliptic PDEs with vector variables in three dimensions....Read more

11

This course was developed by Prof. Krishna Garikipati and Dr. Gregory Teichert, at the University of Michigan in partnership with Ansys. This course focuses on parabolic problems. The problems that will be discussed are linear parabolic PDEs in three dimensions for a scalar variable. Physical problems such as unsteady heat conduction and unsteady mass diffusion are considered here.

12

This course was developed by Prof. Krishna Garikipati and Dr. Gregory Teichert, at the University of Michigan in partnership with Ansys. In this course, we will discuss how to solve linear, hyperbolic partial differential equations for an unknown vector in three dimen...Read more