Journal Articles 

D. M. Williams, C. V. Frontin, E. A. Miller, and D. L. Darmofal "A Family of Symmetric, Optimized Quadrature Rules for Pentatopes," Computers and Mathematics with Applications, 80, (2020) 1405-1420 

D. M. Williams, "An Analysis of Discontinuous Galerkin Methods for the Compressible Euler Equations: Entropy and L2 Stability," Numerische Mathematik, 141, (2019) 1079-1120 

A. S. Wixom, G. S. Walters, S. L. Martinelli, and D. M. Williams, "Generalized Polynomial Chaos with Optimized Quadrature Applied to a Turbulent Boundary Layer Forced Plate," Journal of Computational and Nonlinear Dynamics, 14, (2019) 021010 

D. M. Williams, "An Entropy Stable, Hybridized Discontinuous Galerkin Method for the Compressible Navier-Stokes Equations," Mathematics of Computation, 87, (2018) 95-121 

D. M. Williams, D. S. Kamenetskiy, and P. R. Spalart, "On Stagnation Pressure Increases in Calorically Perfect, Ideal Gases," International Journal of Heat and Fluid Flow, 58, (2016) 40-53 

D. M. Williams, L. Shunn, and A. Jameson, "Symmetric Quadrature Rules for Simplexes Based on Sphere Close Packed Lattice Arrangements," Journal of Computational and Applied Mathematics, 266, (2014) 18-38 

D. M. Williams and A. Jameson, "Energy Stable Flux Reconstruction Schemes for Advection-Diffusion Problems on Tetrahedra," Journal of Scientific Computing, 59, (2014) 721-759 

D. M. Williams, P. Castonguay, P. E. Vincent, and A. Jameson, "Energy Stable Flux Reconstruction Schemes for Advection-Diffusion Problems on Triangles," Journal of Computational Physics, 250, (2013) 53-76 

P. Castonguay, D. M. Williams, P. E. Vincent, and A. Jameson, "Energy Stable Flux Reconstruction Schemes for Advection-Diffusion Problems," Computer Methods in Applied Mechanics and Engineering, 267 (2013) 400-417 

Conference Papers 

D. M. Williams and A. Jameson, "Nodal Points and the Nonlinear Stability of High-Order Methods for Unsteady Flow Problems on Tetrahedral Meshes," AIAA Paper 2013-2830, 43rd AIAA Fluid Dynamics Conference, San Diego, CA, (2013) 

D. M. Williams, P. Castonguay, P. E. Vincent, and A. Jameson, "An Extension of Energy Stable Flux Reconstruction to Unsteady, Non-linear, Viscous Problems on Mixed Grids," AIAA Paper 2011-3405, 20th AIAA Computational Fluid Dynamics Conference, Honolulu, HI, (2011) 

P. Castonguay, D. M. Williams, P. E. Vincent, M. R. Lopez, and A. Jameson, "On the Development of a High-Order, Multi-GPU Enabled, Compressible Viscous Flow Solver for Mixed Grids," AIAA Paper 2011-3229, 20th AIAA Computational Fluid Dynamics Conference, Honolulu, HI, (2011) 

Dissertation 

D. M. Williams, "Energy Stable High-Order Methods for Simulating Unsteady, Viscous, Compressible Flows on Unstructured Grids," Stanford University, (2013)