Stability and accuracy of optimal local non-reflecting boundary conditions

Problems in unbounded domains are often solved numerically by truncating th e infinite domain via an artificial boundary B and applying some boundary c ondition on a, which is called a Non-Reflecting Boundary Condition (NRBC). Recently, a two-parameter hierarchy of optimal local NRBCs of increasing or der has been developed. The optimality is in the sense that the local NRBC best approximates the exact nonlocal Dirichlet-to-Neumann (DtN) boundary co ndition in the L-2 norm for functions in C-infinity. The optimal NRBCs are combined with finite element discretization in the computational domain. He re the theoretical properties of the resulting class of schemes are examine d. In particular, theorems are proved regarding the numerical stability of the schemes and their rates of convergence. (C) 2000 IMACS. Published by El sevier Science B.V, All rights reserved.