The Finite-dimensional Weak Form and Basis Functions — Lesson 1

In this lesson, the focus is on the steps involved in setting up a two-dimensional problem for the linear elliptic PDEs in a scalar variable. These equations are applicable to heat conduction and mass diffusion in two dimensions. With the constitutive relation and boundary conditions, the strong form is written first, then the weak form. Basis functions for linear and bilinear Lagrangian polynomials are written.

Continuing from the previous video, the gradient of the trial solution and weighting functions will be computed first. The inverse of the Jacobian matrix gives the desired terms, and then the assembly of the integrals that need evaluated is completed. Before that, the computation of element integral is shown.