Paola Gervasio  DICATAM  University of Brescia  paola.gervasio_at_unibs.it 

Lesson 1  
06/05/2024. 9.0012.00. Lecture 
Introduction to PDEs. Weak derivatives, the spaces L2 and H1. 1d case: elliptic problems with Dirichlet, Neumann or Robin b.c. and their weak forms. Abstract setting: the LaxMilgram lemma. 
0summary.pdf 1intro.pdf 2funanalysis.pdf 
Lesson 2  
08/05/2024. 9.0012.00. Lecture 
1d case: elliptic problems with nonhomogeneous Dirichlet conditions. Galerkin approximation, Céa Lemma, stability and convergence. P1fem: Lagrangian basis, matrix and right hand side assembling. LegendreGauss quadrature formulas. 
3LGquadrature.pdf 
Lesson 3  
10/05/2024. 9.0012.00. MATLAB/Lecture 
Numerical solution of 1D elliptic problems
with Finite Elements and MATLAB. Error analysis. P2fem. 
FEM1d.zip 4labfem1.pdf 51dfemerror.pdf 6linearsystems.pdf 
Lesson 4  
13/05/2024. 9.0012.00. Lecture 
Weak form of elliptic problems with Dirichlet, Neumann, and mixed b.c. in
2d/3d. Galerkin formulation. Finite Elements discretization. Triangulations. P1 and Q1 FEM. Construction of the linear system. Error estimates. Generalization to higher polynomial degree. A short review of Spectral Element Methods. 
72dfem.pdf 8sem.pdf 
Lesson 5  
15/05/2024. 9.0012.00. MATLAB  Numerical solution of 2d elliptic equations with MATLAB pdetool 
9labfem2d.pdf FEM2d.zip 
Lesson 6  
16/05/2024. 9.0012.00. Lecture/MATLAB 
Parabolic problems: weak formulation. Approximation in space by FEM and in time
by finite differences. Stability and Convergence analysis. Numerical solution of Parabolic problems with MATLAB. 
FEM1d.zip 10labparabolic.pdf 
Lesson 7  
20/05/2024. 9.0012.00. Lecture/MATLAB 
Advection diffusion reaction problems. Artificial diffusion, stramline diffusion, and stabilization techniques. Numerical solution of advectiondiffusion problems. 
FEM1d.zip FEM2d.zip 11labad.pdf 

Paola Gervasio  May 2024 