ELISA CALZOLA

PhD Graduate

PhD program:: XXXIV


supervisor: E. Carlini
advisor: E. Carlini

Thesis title: Semi-Lagrangian schemes for parabolic equations: second order accuracy and boundary conditions

This thesis deals with second order parabolic differential equations and some semi-Lagrangian methods to approximate their solutions. We start with a brief survey of the main theoretical results concerning linear and nonlinear parabolic equations, recalling some existence and uniqueness to the Cauchy problem on the entire space and to the Initial-Boundary value problem with Dirichlet and Neumann type boundary conditions. In the following three chapters, we present our approach to the numerical solution to three different problems. First, we introduce a semi-Lagrangian method for advection-diffusion-reaction systems of equations on bounded domains, with Dirichlet boundary conditions. Afterwards, we present a semi-Lagrangian technique for approximating the solution to Hamilton-Jacobi-Bellman equations on bounded domain, with Neumann-type boundary conditions. Finally, we present a Lagrange-Galerkin approximation of the Fokker-Planck equation, and we show how to apply such a method to obtain a second-order accurate solution to Mean Field Games. Every method is accompanied with numerical simulations.

Research products

  • 11573/1392905 - 2020 - A Fully Semi-Lagrangian Method for the Navier–Stokes Equations in Primitive Variables (02a Capitolo o Articolo)
    BONAVENTURA, LUCA; CALZOLA, ELISA; CARLINI, ELISABETTA; FERRETTI, ROBERTO
  • 11573/1632742 - 2022 - Semi-Lagrangian schemes for parabolic equations: second order accuracy and boundary conditions (07a Tesi di Dottorato)
    CALZOLA, ELISA
  • 11573/1667216 - 2023 - A semi-Lagrangian scheme for Hamilton–Jacobi–Bellman equations with oblique derivatives boundary conditions (01a Articolo in rivista)
    CALZOLA, ELISA; CARLINI, ELISABETTA; DUPUIS, XAVIER; SILVA ALVAREZ, FRANCISCO JOSE'
  • 11573/1552635 - 2021 - Second Order Fully Semi-Lagrangian Discretizations of Advection-Diffusion-Reaction Systems (01a Articolo in rivista)
    CALZOLA, ELISA; CARLINI, ELISABETTA; FERRETTI, ROBERTO

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