Lecture Computational PDEs III (SS 2026)
Theorie und Numerik partieller Differentialgleichungen III

Basic information

• Lecture and exercises: Dietmar Gallistl
• Friedolin info
• Dates: see table below
• Required preliminaries: finite element method; linear functional analysis
  
• This is a 3 ECTS course. Lectures are scheduled for Fridays, 8:15-9:45.
• Oral exams on individual appointment.

Syllabus/topics

• Elliptic PDE in nondivergence form

Literature

• [GT98] Gilbarg/Trudinger. Elliptic PDE of second order. Springer, 1998.
• [MPS00] Maugeri/Palagachev/Softova. Elliptic and parabolic equations with discontinuous coefficients. Wiley, 2000.
• [SS13] I. Smears, E. Süli. Discontinuous Galerkin finite element approximation of nondivergence form elliptic equations with Cordes coefficients, SIAM Journal on Numerical Analysis 51(4), pages 2088--2106, 2013. doi:10.1137/120899613 download
• [SS14] I. Smears, E. Süli. Discontinuous Galerkin finite element approximation of Hamilton–Jacobi–Bellman equations with Cordes coefficients, SIAM Journal on Numerical Analysis 52(2), pages 993--1016, 2014. doi:10.1137/130909536 download
• [T25] Finite element approximation for uniformly elliptic linear PDE of second order in nondivergence form, Math. Comp. 94, pages 1043--1064. 2025. doi:10.1090/mcom/3966 download
• [G18] D. Gallistl. Mixed finite element approximation of elliptic equations involving high-order derivatives, 2018. download