Structure-preserving algorithms for nonlinear PDEs
- Arbitrarily high-order entropy stable finite-difference (volume) schemes for multi-dimensional hyperbolic systems of conservation laws.
- Arbitrarily high-order entropy stable space-time adaptive Discontinuous Galerkin (DG) finite element methods for multi-dimensional hyperbolic systems of conservation laws.
- Stable and Convergent Spectral Viscosity and Finite-difference Projection methods for Incompressible Euler and Navier-Stokes equations.
- Equilibrium-preserving Well-balanced schemes for systems of balance laws.
- Finite difference schemes with well-controlled dissipation for resolving small-scale dependent shock waves in non-strictly hyperbolic and non-conservative hyperbolic systems.
Selected Publications
U.S. Fjordholm, S. Mishra and E. Tadmor, Arbitrarily high order accurate entropy stable essentially non-oscillatory schemes for systems of conservation laws, SIAM Jl. Num. Anal, 50(2), 2012, 544-573.
U.S. Fjordholm, S. Mishra and E. Tadmor, ENO reconstruction and ENO interpolation are stable, Found. Comput. Math, 13 (2), 2013, 139-159.
A. Hiltebrand and S. Mishra, Entropy stable shock capturing streamline diffusion space-time discontinuous Galerkin (DG) methods for systems of conservation laws, Numer. Math, 126 (1), 2014, 103-151.
U.S. Fjordholm, S. Mishra and E. Tadmor, Energy preserving and energy stable schemes for shallow water equations with bottom topography, Jl. Comput. Phys, 230, 2011, 5587-5609.
P. LeFloch and S. Mishra, Numerical methods with controlled dissipation for small-scale dependent shocks, Acta Numerica, 23, 2014, 743-816.