Publications

A. Celaya, Keegan L.A. Kirk, D. Fuentes, and B. Rivière. Solutions to elliptic and parabolic problems via finite difference based unsupervised small linear convolutional neural networks. (Link)

Keegan L.A. Kirk and B. Rivière. A combined mixed hybrid and hybridizable discontinuous Galerkin method for flow and transport. 

Keegan L.A. Kirk, R. Masri, and B. Rivière. Numerical analysis of a hybridized discontinuous Galerkin method for the Cahn–Hilliard problem. IMA Journal of Numerical Analysis, 2023. (Link)

Keegan L.A. Kirk, T. L. Horváth, and S. Rhebergen. Analysis of an exactly mass conserving space-time hybridized discontinuous Galerkin method for the time-dependent Navier-Stokes equations. Mathematics of Computation, 92(340):525–556, 2023. (Link)

Keegan L.A. Kirk, A. Çesmelioglu, and S. Rhebergen. Convergence to weak solutions of a space-time hybridized discontinuous Galerkin method for the incompressible Navier–Stokes equations. Mathematics of Computation, 92(339):147–174, 2023. (Link)

K. R. Bryenton, A. R. Cameron, Keegan L.A. Kirk, N. Saad, P. Strongman, and N. Volodin. On the solutions of second-order differential equations with polynomial coefficients: Theory, algorithm, application. Algorithms, 13(11), 2020. (Link)

Keegan L.A. Kirk and S. Rhebergen. Analysis of a pressure-robust hybridized discontinuous Galerkin method for the stationary Navier-Stokes equations. Journal of Scientific Computing, 81(2):881–897, 2019. (Link)

Keegan L.A. Kirk, T. L. Horváth, A. Çesmelioglu, and S. Rhebergen. Analysis of a spacetime hybridizable discontinuous Galerkin method for the advection-diffusion problem on time-dependent domains. SIAM Journal on Numerical Analysis, 57(4):1677–1696, 2019. (Link)

Keegan L.A. Kirk, K. R. Bryenton, and N. Saad. A note on the generalized and universal associated Legendre equations. Communications in Theoretical Physics, 70(1), 2018. (Link)