Stability and accuracy of optimal local non-reflecting boundary conditions Original Research Article

Problems in unbounded domains are often solved numerically by truncating the infinite domain via an artificial boundary View the MathML source and applying some boundary condition on View the MathML source, which is called a Non-Reflecting Boundary Condition (NRBC). Recently, a two-parameter hierarchy of optimal local NRBCs of increasing order has been developed. The optimality is in the sense that the local NRBC best approximates the exact nonlocal Dirichlet-to-Neumann (DtN) boundary condition in the L2 norm for functions in C∞. The optimal NRBCs are combined with finite element discretization in the computational domain. Here the theoretical properties of the resulting class of schemes are examined. In particular, theorems are proved regarding the numerical stability of the schemes and their rates of convergence.