Weak Form of the Partial Differential Equation - Lesson 5

The discussion continues the analytical solutions and needs for approximate solutions is introduced. Use of the finite difference method to solve any differential equation is introduced. The weak form of a linear elliptic partial differential equation is introduced, and the weak form is solved with one Dirichlet boundary condition.

The weak form is the basis of the finite element method and other variational-based numerical methods. The equivalence between the strong and the weak form is demonstrated. A strong form will lead to a weak form. The weighting function is introduced.