• BS, Aerospace Engineering, University of Michigan, 2008
• MS, Aeronautics and Astronautics, Stanford University, 2012
• Ph D, Aeronautics and Astronautics, Stanford University, 2013

Journal Articles

David M Williams and Qingguo Hong, 2024, "Generalized Korn's inequalities for piecewise H2 vector fields", Mathematics of Computation

Jude T Anderson, David M Williams and Andrew Corrigan, 2023, "Surface and hypersurface meshing techniques for space-time finite element methods", Computer-Aided Design, 163, pp. 1-16

Edward A Miller, Xi Chen and David M Williams, 2022, "Versatile mixed methods for non-isothermal incompressible flows", Computers and Mathematics with Applications, 125, (1), pp. 150-175

Miroslav Petrov, Todor Todorov, Gage S Walters, David M Williams and Freddie D Witherden, 2022, "Enabling four-dimensional conformal hybrid meshing with cubic pyramids", Numerical Algorithms, pp. 1-39

Cory V Frontin, Gage S Walters, Freddie D Witherden, Carl W Lee, David M Williams and David L Darmofal, 2021, "Foundations of space-time finite element methods: polytopes, interpolation, and integration", Applied Numerical Mathematics, 166, pp. 92-113

Karthik Ganeshan and David M Williams, 2021, "An implicit discontinuous Galerkin finite element discrete Boltzmann method for high Knudsen number flows", Physics of Fluids, 33, (3), pp. 032019

David M Williams and Gage S Walters, 2020, "Integration bounds for the regular simplex in n-dimensional space", International Journal of Mathematical Education in Science and Technology, 1, pp. 1-16

Xi Chen and David Michael Williams, 2020, "Versatile mixed methods for the incompressible Navier-Stokes equations", Computers and Mathematics with Applications, 80, pp. 1555-1577

David M Williams, Cory V Frontin, Edward A Miller and David L Darmofal, 2020, "A family of symmetric, optimized quadrature rules for pentatopes", Computers and Mathematics with Applications, 80, pp. 1405-1420

David Michael Williams, 2019, "An analysis of discontinuous Galerkin methods for the compressible Euler equations: entropy and L2 stability", Numerische Mathematik, 141, pp. 1079-1120

Andrew S Wixom, Gage S Walters, Sheri L Martinelli and David Michael Williams, 2019, "Generalized polynomial chaos with optimized quadrature applied to a turbulent boundary layer forced plate", Journal of Computational and Nonlinear Dynamics, 14, pp. 1-9

David Michael Williams, 2018, "An entropy stable, hybridizable discontinuous Galerkin method for the compressible Navier-Stokes equations", Mathematics of Computation, 87, pp. 95-121

David Michael Williams, Dmitry S Kamenetskiy and Philippe R Spalart, 2015, "On stagnation pressure increases in calorically perfect, ideal gases", International Journal of Heat and Fluid Flow, 58, pp. 40-53

David Michael Williams, L. Shunn and A. Jameson, 2014, "Symmetric quadrature rules for simplexes based on sphere close packed lattice arrangements", Journal of Computational and Applied Mathematics, 266, pp. 18-38

David Michael Williams and A. Jameson, 2014, "Energy stable flux reconstruction schemes for advection–diffusion problems on tetrahedra", Journal of Scientific Computing, 59, pp. 721-759

P. Castonguay, David Michael Williams, P. E. Vincent and A. Jameson, 2013, "Energy stable flux reconstruction schemes for advection–diffusion problems", Computer Methods in Applied Mechanics and Engineering, 267, pp. 400-417

David Michael Williams, P. Castonguay, P. E. Vincent and A. Jameson, 2013, "Energy stable flux reconstruction schemes for advection–diffusion problems on triangles", Journal of Computational Physics, 250, pp. 53-76

Conference Proceedings

Service to Penn State:

Service to External Organizations:

• Organizing Conferences and Service on Conference Committees, Administrator, Computational Fluid Dynamics (CFD) Conference Administrative Organizer, American Institute of Aeronautics and Astronautics, September 2021 - May 2022

• Organizing Conferences and Service on Conference Committees, Chairperson, CFD Conference Organizer, American Institute of Aeronautics and Astronautics, September 2020 - May 2021

• Organizing Conferences and Service on Conference Committees, Committee Member, Fluid Dynamics Technical Committee, American Institute of Aeronautics and Astronautics, February 2019

• Organizing Conferences and Service on Conference Committees, Co-Organizer, Minisymposium Planning, International Association on Computational Mechanics, March 2019 - April 2019