Advanced Discretization Methods (PhD)

The course examines the development and analysis of spectral methods for the solution of time-dependent partial differential equations. Topics include key elements of approximation and stability theory for Fourier and polynomial spectral methods, as well as temporal integration and numerical aspects.

REFERENCES

• Spectral methods for time-dependent problems implementation, post-processing and error estimates; J. Hesthaven, S. Gottlieb, D. Gottlieb
• Hybrid and Mixed Finite Element Methods; Atluri SN, Gallagher RH and Zienkiewicz OC.
• Connection between finite volume and mixed finite element methods: Baranger J, Maitre J-F and Oudin F., - Finite Elements., Theory, Fast Solvers and Applications in Solid Mechanics; Braess D.
• Nonconforming finite element methods for the equations of linear elasticity; Falk RS.
• A family of mixed finite elements for the elasticity problem; Stenberg R.