In this paper, we apply the Paired-Explicit Runge-Kutta (P-ERK) schemes by Vermeire et
al.[1],[2] to dynamically partitioned systems arising from adaptive mesh refinement. The P …

Many mathematical models of continuum mechanics are derived from integral conservation
laws. Examples of such models include the Euler and Navier–Stokes equations of fluid …

We introduce a general framework for enforcing local or global maximum principles in high-
order space-time discretizations of a scalar hyperbolic conservation law. We begin with …

We analyze a least-squares strong-form kernel collocation formulation for solving second-
order elliptic PDEs on smooth, connected, and compact surfaces with bounded geometry …

We present a number of new contributions to the topic of constructing efficient higher-order
splitting methods for the numerical integration of evolution equations. Particular schemes …

We analyze monotonicity, strong stability and positivity of the TR-BDF2 method, interpreting
these properties in the framework of absolute monotonicity. The radius of absolute …

A finite volume approximation of the scalar hyperbolic conservation law or advection–
diffusion equation is given. In the context of the method of lines, the space discretization …

Many interesting applications of hyperbolic systems of equations are stiff, and require the
time step to satisfy restrictive stability conditions. One way to avoid small time steps is to use …

Accurate and efficient simulation of multiphase flow in heterogeneous porous media
motivates the development of space-time multiscale strategies for the coupled nonlinear flow …

Many important differential equations model quantities whose value must remain positive or
stay in some bounded interval. These bounds may not be preserved when the model is …