Numerical Methods for Civil Engineering Notes of the Course

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