Franco BREZZI

Scientific Interests

His scientific interests are mainly concentrated in the field of Numerical Methods for Partial Differential Equations.

In particular, from the point of view of methodological tools, he works mainly on Finite Element Methods (of various kinds).

From the applicative point of view, he is mostly interested in problems coming from various Engineering fields, such as Structural Mechanics, Fluid Mechanics, and Electromagnetics.

In particular he worked on the following topics

Existence, uniqueness, and regularity of the solutions of boundary value problems for P.D.E.

Numerical solution of linear elliptic problems with irregular data.

Basic properties of finite element methods (in particular, non-standard f.e .methods, as mixed, hybrid etc.)

Approximation of variational inequalities and free boundary problems.

Behaviour and approximation properties of finite dimensional discretizations of bifurcation problems.

Theoretical and numerical problems in semiconductor device simulations.

Finite element analysis of plates and shells.

Domain decomposition methods.

Stabilization techniques in finite element formulations.

Residual-free bubbles and subgrid-scale simulations.

Approximation of eigenvalues of problems in mixed form.

Discontinuous finite element methods.

Mimetic finite differences.

Virtual Element Methods.

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