AIMS Seminar | Alex Bercik (University of Toronto)
Nov 17, 2025
11:30AM to 12:30PM
Date/Time
Date(s) - 17/11/2025
11:30 am - 12:30 pm
Speaker: Alex Bercik (University of Toronto)
Location: Hamilton Hall, Room 312
Title: Provable Numerical Stability Without the Variational Crimes: An Introduction to Summation-By-Parts Methods for PDEs
Abstract: Summation-by-parts (SBP) methods provide a powerful algebraic framework for constructing high-order discretizations of partial differential equations that rigorously mimic various properties of the continuous problem. By enforcing a discrete form of integration by parts, SBP schemes enable discrete analogues of conservation, stability, and other structure-preserving proofs—without relying on assumptions such as exact integration often required in finite-element and discontinuous Galerkin formulations. SBP methods can be expressed in finite-difference, finite-volume, or finite-element form, allowing them to inherit the geometric flexibility, h-p adaptivity, and analytical tools developed within each of these frameworks.