# The Matrix-vector Weak Form — Lesson 8

In this lesson, we are continuing with developing a matrix-vector weak form for the linear elliptic PDE with scalar variables in 3D. We will complete assembling the matrix-vector weak form and discuss associated issues which arise mainly from the fact that we are looking at the problems in 3D. We will discuss assembling element-level integrals to create final matrix-vector equations.

In this video, we are continuing with assembling element-level matrix-vector representation into a global matrix-vector weak form. We will look at the element-level contributions and understand how to map them into a global vector. This is easy to do in a 1D problem, but more difficult in a 3D problem. Mesh connectivity will be addressed in this lesson as well.

We will continue assembling global finite element equations in a matrix-vector form. Once we have the mesh connectivity information and the local conductivity matrix for each element, it is fairly easy to assemble the global conductivity matrix, which is discussed in the following lessons. We also discuss how to account for the Dirichlet boundary conditions while solving the equations.

Corrections to Boardwork