Difference approximations for wave equations via finite elements. I. Construction and performance

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Abstract
Many practical applications of wave equations involve media in which there are interfaces, or discontinuities in material properties. The accurate numerical representation of these interfaces is important in mathematical models. One can develop generalizations of standard finite‐difference methods that accommodate sharp interfaces by modifying a straightforward finite‐element approach. In two space dimensions, these methods yield explicit, 5‐point or 9‐point difference schemes that accurately capture reflection, transmission, and refraction at interfaces. The approach also extends readily to the simulation of waves in elastic media. A companion article presents an error analysis for the approach. © 1995 John Wiley & Sons, Inc.