A general framework for constructing constraint-preserving numerical methods is presented and applied to a multidimensional divergence-constrained advection equation. This equation is part of a set of ...

An energy-based discontinuous Galerkin method for the advective wave equation is proposed and analyzed. Energy-conserving or energy-dissipating methods follow from simple, mesh-independent choices of ...

The Helmholtz equation is a fundamental partial differential equation that underpins the analysis of wave propagation, acoustic scattering and electromagnetic phenomena. Its numerical solution is ...

In this paper we introduce two methods for the efficient and accurate numerical solution of Black–Scholes models of American options: a penalty method and a front-fixing scheme. In the penalty ...