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 concentration and mass influx with respect to mass diffusion. Then we will derive an equivalent infinite-dimensional weak form from the strong form of steady-state heat conduction and mass diffusion.

After that, we derive an equivalent finite-dimensional weak form from the infinite-dimensional weak form. We also discuss a general eight-node brick element, or hexahedral element, and the trilinear basis functions used in its formulation. In the following lessons, we will talk about the Jacobian of the map, followed by the integrals in terms of the degree of freedom of an element. Lastly, we will conclude with the matrix-vector weak form. This course was developed by Prof. Krishna Garikipati and Dr. Gregory Teichert, at the University of Michigan, in partnership with Ansys.