We formulate and analyze a discontinuous finite element method for hyperbolic equations in R-2, applicable over a rectangular mesh, and show that the method can be extended to R-N, N > 2, in a stable manner. An optimal O(h(n+1)) error estimate is derived for nth degree approximation over a mesh of size h. The R-2 method is closely related to a continuous tensor product finite element method of Winther [Math. Comp., 36 (1981), pp. 65-86] which, though stable in two dimensions, allows polynomially growing instabilities when extended to higher dimension. The methods under consideration can be viewed as finite element generalizations of a box scheme of Wendroff [J. Soc. Indust. Appl. Math., 8 (1960), pp. 549-555]. [References: 10]
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