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- Phillip Colella, Milo R. Dorr, Jeffrey A. F. Hittinger, Daniel F. Martin
- J. Comput. Physics
- 2011

We present an approach for constructing finite-volume methods of any order of accuracy for control-volume discretizations of space defined as the image of a smooth mapping from a rectangularâ€¦ (More)

- Jeffrey W. Banks, Jeffrey A. F. Hittinger
- IEEE Transactions on Plasma Science
- 2010

Methods for the numerical discretization of the Vlasov equation should efficiently use the phase-space discretization and should introduce only enough numerical dissipation to promote stability andâ€¦ (More)

- Peter McCorquodale, Milo R. Dorr, Jeffrey A. F. Hittinger, Phillip Colella
- J. Comput. Physics
- 2015

We present an approach to solving hyperbolic conservation laws by finitevolume methods on mapped multiblock grids, extending the approach of Colella, Dorr, Hittinger, and Martin (2011) for grids withâ€¦ (More)

- Jeffrey A. F. Hittinger, Jeffrey W. Banks
- J. Comput. Physics
- 2013

Direct discretization of continuum kinetic equations, like the Vlasov equation, are under-utilized because the distribution function generally exists in a high-dimensional (>3D) space andâ€¦ (More)

- Milo R. Dorr, Ron H. Cohen, +4 authors Martin
- 2011

We describe our progress in the development of a fourth-order, finite-volume discretization of a nonlinear, full-f gyrokinetic Vlasov-Poisson system in mapped coordinates. The approach treats theâ€¦ (More)

For many problems in astrophysics and space sciences, it is desirable to compute solutions in a way that preserves spherical symmetry, so that the dynamics of small perturbations about theâ€¦ (More)

Numerical error estimation for time dependent hyperbolic problems is challenging for theoretical and practical reasons. In these systems, error can propagate long distances and produce effects farâ€¦ (More)

To simulate accurately and efficiently aerospace-type flows using solely first-order PDE models, new numerical methods may be required to overcome difficulties introduced by the model. We consider aâ€¦ (More)

- Jeffrey M. Connors, Jeffrey W. Banks, Jeffrey A. F. Hittinger, Carol S. Woodward
- SIAM J. Numerical Analysis
- 2013

Abstract. This paper is concerned with the computation of numerical discretization error for uncertainty quantification. An a posteriori error formula is described for a functional measurement of theâ€¦ (More)