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Sep 2025
A decoupled and structure-preserving direct discontinuous Galerkin method for the Keller–Segel model
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Open access
Sep 2026
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A Reynolds-Semi-Robust, Globally Divergence-Free HDG Method for the Smagorinsky Model
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Open access
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Preconditioning a Hybridizable Discontinuous Galerkin Method for Navier–Stokes at High Reynolds Number
Abstract. We introduce a preconditioner for a hybridizable discontinuous Galerkin discretization of the linearized Navier–Stokes equations at high Reynolds number. The preconditioner is based on an augmented Lagrangian (AL) approach of the full discretization. Unlike standard grad-div type augmentation, however, we co...
A. Lindsay, S. Rhebergen, B. Southworth
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Open access
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A novel penalty-based least-squares discontinuous Galerkin (LS-DG) method for time-dependent Stokes equations
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Analyticity of the data-to-solution map for a stationary Navier-Stokes fluid-structure interaction problem
We consider a stationary fluid--structure interaction problem in which the steady Navier--Stokes equations are coupled, through a free elastic interface, with a clamped Euler-Bernoulli beam equation. Using a complexification of the fixed-domain formulation and the holomorphic implicit function theorem, we prove that, i...
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