• March 2026: our preprint "Volume Term Adaptivity for Discontinuous Galerkin Schemes" with Daniel Doehring, Jesse Chan, Hendrik Ranocha, Michael Schlottke-Lakemper, Manuel Torrilhon, Gregor Gassner is now online at https://arxiv.org/abs/2603.24189. This work introduces "volume term adaptivity", where the discretization of the DG volume term is modified dynamically based on several criteria, such as entropy change, heuristic shock capturing sensors, and hybrid strategies between the two.
  
  

• March 2026: Jesse Chan gave keynote talks at SCALA 2026 and TRUDI 2026
  
  

• February 2026: our preprint "On the choice of viscous discontinuous Galerkin discretization for entropy correction artificial viscosity methods" with Samuel Van Fleet is now online at https://arxiv.org/abs/2602.23210. This work shows that the choice of viscous discretization for artificial viscosity-based entropy correction methods matters. In particular, we show that when a local DG method is used, the artificial viscosity does not result in a stricter explicit CFL condition while also exhibiting a superconvergence property for sufficiently regular solutions. Finally, we demonstrate that this entropy correction approach is contact-preserving and minimally dissipative compared with sensor-based shock capturing.
  
  

• February 2026: Todd Arbogast, Leszek Demkowicz, and Jesse Chan organized the 2026 Finite Element Rodeo at UT Austin.
  
  

• February 2026: Jesse Chan gave a talk in the Scientific Computing Seminar at Brown University.
  
  

• November 2025: our paper "A robust first order meshfree method for time-dependent nonlinear conservation laws" with Samuel Kwan is now online. This work describes a simple method for constructing robust mesh-free discretizations using a summation-by-parts framework (which are computed and optimized using a simple and efficient two-step process) and a flux differencing formulation. Samuel is now a PhD student in IE/OR at U. Chicago; this work was done while Samuel was an undergraduate in our group.
  
  

• October 2025: the preprint "Efficient and Robust Caratheodory-Steinitz Pruning of Positive Discrete Measures" is available on arXiv now, and describes an new efficient implementation of a deterministic algorithm for calculating a moment-preserving reduced quadrature rule from a high-dimensional reference quadrature. The algorithm has been applied to both cut-cell quadratures and hyper-reduction in projection-based reduced order models.
  
  

• With Tan Bui-Thanh, Jesse Chan organized the 2025 Annual SIAM TXLA Sectional Meeting from Sept. 26-28 at UT Austin and the Oden Institute. This year, the conference had over 350 participants, 43 minisymposia, 4 plenary talks, a career panel, and mini-tutorial sessions.
  
  

• September 2025: the arXiv preprint of "Entropy stable finite difference methods via entropy correction artificial viscosity and knapsack limiting" by alumnus of the group Brian Christner is now online. This work extends two recently developed techniques for enforcing an entropy inequality (entropy correction artificial viscosity and knapsack limiting) to finite difference methods using a discrete graph-based artificial viscosity. The resulting scheme is high order accurate, and the knapsack limiting variant is able to preserve positivity for problems such as the LeBlanc shock tube and Woodward-Collela blast wave.
  
  

• September 2025: Jesse Chan gave a virtual talk in the Department of Mathematics "Modeling and Computation" seminar at the University of Arizona.

• August 2025: Jesse Chan gave a talk in the Babuska Forum at the Oden Institute.
  
  

• July 2025: the arXiv preprint of "Entropy Stable Nodal Discontinuous Galerkin Methods via Quadratic Knapsack Limiting" with graduate student Brian Christner is now online. This work generalizes our previous paper with Yimin Lin on enforcing an entropy inequality directly using subcell limiting. Lin computed optimal flux corrected transport (FCT) type limiting coefficients to enforce both invariant domain constraints and a cell entropy inequality. These optimal FCT coefficients are computed by solving a linear knapsack problem, whose solution can be computed using a simple and efficient deterministic algorithm.
  
  In this new preprint, Christner introduces a generalization of this approach using a quadratic knapsack problem, which significantly improves both the temporal accuracy and efficiency of the resulting discretization while retaining the efficiency and flexibility of the original knapsack problem. In particular, Christner shows that this new knapsack problem can be reduced to scalar root-finding problem with an efficient derivative formula and guaranteed convergence. We also demonstrate that the knapsack limiting entropy stable DG method is locally linearly stable, addressing an open theoretical issue with some high order entropy stable DG methods.
  
  

• July 2025: PhD student Ray Qu and Jesse Chan both gave talks at the ICOSAHOM 2025 and USNCCM 18 meetings. Jesse Chan's talk focused on recent work on entropy correction artificial viscosity for high order DG methods, while Ray Qu's talk was on recent work utilizing model reduction techniques for the stochastic finite volume method, a hyperbolicity-preserving method for uncertainty quantification for nonlinear conservation laws.
  
  

• July 2025: the arXiv preprint of "Model order reduction techniques for the stochastic finite volume method" with Ray Qu (Rice) and Svetlana Tokareva (LANL) is now available. The stochastic finite volume method (SFVM) developed by Tokareva, Abgrall, and others is an uncertainty quantification (UQ) technique for hyperbolic PDEs which preserves hyperbolicity. However, the resulting discretization can become very expensive for high dimensional stochastic parameter spaces.
  
  In this preprint, we utilize model reduction techniques (a reduced stochastic basis and hyper-reduction) to reduce the dimensionality of the stochastic part of the resulting system for 1D nonlinear conservation laws. In particular, we note that the reduced system does not require constructing the higher-dimensional SFVM system, and can be constructed purely by sampling deterministic 1D simulations.
  
  

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