Final projects#

Seminars#

Seminars based on articles#

Your presentation should include all proofs, and a brief introduction for those topics that we did not do in class.

  1. Babuska \(\Longleftrightarrow\) Brezzi?

  2. On some techniques for approximating boundary conditions in the finite element method

  3. Analysis of the Shifted Boundary Method for the Poisson Problem in General Domains

  4. Static Condensation, Hybridization, and HDG Methods

  5. A unified study of continuous and discontinuous Galerkin methods

Seminars based on advanced theory#

Your task is to prepare a one-hour lecture on one of the following topics:

  1. Drift-diffusion-reaction problems (chap. 8 of Quarteroni and Valli [QV94])

    • Well posedness

    • Discretization

    • Inconsistent stabilizations (i.e., artificial diffusion)

    • Consistent stabilizations (i.e., GLS, SUPG)

  2. A Posteriori Error Estimates and Adaptive Meshes (chap. 10 of Ern and Guermond [EG04])

    • (A review of) Residual-Based Error Estimates (done in class)

    • Hierarchical Error Estimates

    • Duality-Based Error Estimates

Coding projects#

  1. Implement the shifted boundary method (starting from step-60)

  2. Implement the SQH scheme to Solve Nonsmooth PDE Optimal Control Problems

  3. Implement a coupled Laplace-Beltrami – Poisson problem (step-38 + step-6)

  4. Add support for Chapel in deal.II* (step-64 con chapel)

  5. Implement step-64 using Kokkos.

  6. A time dependent problem, using SUNDIALS, and Nitsche boundary conditions.