Approximation methods

Program:

• numerical solution of linear systems (direct and iterative methods, conjugate gradient,...).
• One-dimensional boundary value problems.
• Boundary value problems in higher dimensions: Galerkin method, finite elements, interpolation error, error estimates.
• Elliptic equations: L2 error estimate.
• Parabolic and hyperbolic equations.
• Computational problem: mesh generation, matrix assembly,...
• Adaptive methods for PDEs.
• Numerical optimization: Newton-like methods, simplex method.

References:

• V. Comincioli, Analisi Numerica, Metodi Modelli Applicazioni. McGraw Hill Libri Italia, Milano, 1990.
• A. Quarteroni e A. Valli, Numerical approximation of partial differential equations. Springer, 1994.
• C. Johnson, Numerical solution of partial differential equations by the finite element method. Cambridge university press, Cambridge 1990.