Titlebook: Numerical Models for Differential Problems; Alfio Quarteroni Textbook 20173rd edition Springer International Publishing, AG 2017 PDE.analy

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Diffusion-transport-reaction equations,In this chapter we analyze the conditions ensuring the existence and uniqueness of the solution to problem (13.1).We also consider the Galerkin method, illustrate its difficulties in providing stable solutions in the presence of boundary layers, and finally propose alternative discretization methods for the approximation of (13.1).

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Finite elements and spectral methods for hyperbolic equations,In this chapter we will illustrate how to apply Galerkin methods, and in particular the finite element method and the spectral one, to the spatial and/or temporal discretization of scalar hyperbolic equations.We will treat both continuous as well as discontinuous finite elements.

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Springer International Publishing, AG 2017

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Isogeometric analysis,promise to close the current gap between Computer Aided Design (CAD) procedures and computational modeling of PDEs (as outlined e.g. in Sec. 8.1) by recognizing that the meshing procedure of the computational domain is indeed a major bottleneck in Engineering practice.

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Discontinuous element methods (DG and mortar), and then generalize to the case of diffusion and transport problems (see Chapter 13). To maintain the presentation general we will consider a partition of the computational domain into disjoint subdomains that may be either finite or spectral elements.