Mass-conservative and positivity preserving second-order semi-implicit methods for high-order parabolic equations

Implicit Positivity-preserving High Order

Positivity-preserving discontinuous Galerkin (DG) methods for solving hyperbolic 5 conservation laws have been extensively studied in the last several years. But nearly all the devel6 oped schemes are coupled with explicit time discretizations. Explicit discretizations suffer from the 7 constraint for the Courant-Friedrichs-Levis (CFL) number. This makes explicit methods impractical 8 for probl...

Conservative high order positivity-preserving discontinuous Galerkin methods for linear hyperbolic and radiative transfer equations

We further investigate the high order positivity-preserving discontinuous Galerkin (DG) methods for linear hyperbolic and radiative transfer equations developed in [14]. The DG methods in [14] can maintain positivity and high order accuracy, but they rely both on the scaling limiter in [15] and a rotational limiter, the latter may alter cell averages of the unmodulated DG scheme, thereby affect...

A second-order positivity preserving scheme for semilinear parabolic problems

In this paper we study the convergence behaviour and geometric properties of Strang splitting applied to semilinear evolution equations. We work in an abstract Banach space setting that allows us to analyse a certain class of parabolic equations and their spatial discretizations. For this class of problems, Strang splitting is shown to be stable and second-order convergent. Moreover, it is show...

Positivity preserving high-order local discontinuous Galerkin method for parabolic equations with blow-up solutions

Article history: Received 13 October 2014 Received in revised form 17 January 2015 Accepted 18 February 2015 Available online 2 March 2015

Implicit Positivity-Preserving High-Order Discontinuous Galerkin Methods for Conservation Laws