Abstract:
This text contains the notes of the course “Numerical Methods in Civil Engineering”, which I have been helding (in Italian) over the last eight years for the MSc in
Civil Engineering at Politecnico di Milano. The material is organized into 6 parts:
• Part I: Foundations (Chapts. 1, 2 and 3)
• Part II: Elliptic Problems (Chapts. 4 and 5)
• Part III: The GFEM for Elliptic Problems in 1D and 2D (Chapts. 6 and 7)
• Part IV: The GFEM for Linear Elasticity (Chapts. 8 and 9)
• Part V: Examination Problems with Solution (Chapt. 10)
• Part VI: Appendices (A, B and C)
Specifically:
• Chapts. 1, 2 and 3 provide an introduction to Numerical Mathematics, Numerical Linear Algebra and Approximation Theory.
• Chapts. 4 and 5 illustrate the weak formulation of a boundary value problem and its numerical approximation using the Galerkin Finite Element
Method (GFEM).
• Chapts. 6 and 7 address the numerical study of 1D model problems and
the implementation in 2D of the finite element model for an advectiondiffusion-reaction boundary value problem.
• Chapts. 8 and 9 deal with the weak formulation and GFE approximation
of the Navier-Lame equations for linear isotropic elasticity in compressible `
and incompressible regimes.
• Chapt. 10 illustrates the complete solution of exercises recently proposed
in class exams at the end of the Course.
• Appendices A, B and C give a short review of the essentials in Linear
Algebra, Functional Analysis and D
