Xiangxiong Zhang, Department of Mathematics, Purdue University Monotonicity in high order accurate schemes for diffusion operators with applications to compressible Navier-Stokes equations For gas dynamics equations such as compressible Euler and Navier-Stokes equations, preserving the positivity of density and pressure without losing conservation is crucial to stabilize the numerical computation. The L1-stability of mass and energy can be achieved by enforcing the positivity of density and pressure during the time evolution. However, high order schemes do not preserve the positivity. It is difficult to enforce the positivity without destroying the high order accuracy and the local conservation in an efficient manner for time-dependent gas dynamics equations. For explicit time discretizations, we show that any high order finite volume type scheme including discontinuous Galerkin method satisfies a weak monotonicity property, which can be used to enforce positivity. This allows us to obtain the first high order positivity-preserving schemes for compressible Navier-Stokes equations. For implicit time discretizations, it is a much harder problem which is related to the fact that second order centered difference and piecewise linear finite element method on triangular meshes... https://calendar.colorado.edu/event/computational_math_seminar_-_xiangxi...