194 citations · 355 across the 12 of their papers we have counts for
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Implicit multistage two-derivative discontinuous Galerkin schemes for viscous conservation laws
Alexander Jaust, Jochen Schütz, David C. Seal
In this paper we apply implicit two-derivative multistage time integrators to viscous conservation laws in one and two dimensions. The one dimensional solver discretizes space with…
A high-order positivity-preserving single-stage single-step method for the ideal magnetohydrodynamic equations
Andrew J. Christlieb, Xiao Feng, David C. Seal +1
We propose a high-order finite difference weighted ENO (WENO) method for the ideal magnetohydrodynamics (MHD) equations. The proposed method is single-stage, single-step, maintains…
Method of lines transpose: High order L-stable O(N) schemes for parabolic equations using successive convolution
Matthew F. Causley, Hana Cho, Andrew J. Christlieb +1
We present a new solver for nonlinear parabolic problems that is L-stable and achieves high order accuracy in space and time. The solver is built by first constructing a single-dim…
A Simple and Effective High-Order Shock-Capturing Limiter for Discontinuous Galerkin Methods
Scott A. Moe, James A. Rossmanith, David C. Seal
The discontinuous Galerkin (DG) finite element method when applied to hyperbolic conservation laws requires the use of shock-capturing limiters in order to suppress unphysical osci…
Explicit Strong Stability Preserving Multistage Two-Derivative Time-Stepping Schemes
Andrew J. Christieb, Sigal Gottlieb, Zachary J. Grant +1
High order strong stability preserving (SSP) time discretizations are advantageous for use with spatial discretizations with nonlinear stability properties for the solution of hype…