An improved projection method

Strictly stable high-order accurate finite difference approximations are derived, for linear initial boundary value problems. The boundary closures are based on the diagonal-norm summation-by-parts framework and the boundary conditions are imposed using an improved projection method. The improved projection method removes some of the numerical issues with the previously derived (here referred to as traditional) projection method. The finite difference approximations lead to fully explicit ODE systems. The accuracy and stability properties are demonstrated for linear hyperbolic and parabolic problems in 1D and 2D. In particular we study the problem where initial and boundary data are inconsistent, that causes the traditional projection method to fail. Comparisons are made also with weak (penalty) enforcement of boundary conditions.