High Order finite difference methods for the wave equation with T-junction grid interfaces

Abstract: We investigate higher order SBP-SAT discretizations of the wave equation for T-junction domains. We indicate stability for our discretization for fourth order operators. We construct a differently formulated proof for stability for a previously constructed discretization of the wave equation for interface domains. We construct non-conforming discretizations of both of the above domains, proving stability for the interface domain and indicating it for the T-junction domain. We construct a fourth order modified equation method for time discretization of second order equations, and rudimentarily test it against fourth order Runge Kutta.