Stability and Phase Speed for Various Finite Element Formulations of the Advection Equation
Williams, R. T.
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This paper analyzes the stability and accuracy of various finite element approximations to the linearized two-dimensional advection equation. Four triangular elements with linear basis functions are included along with a rectangular element with bilinear basis functions. In addition, second-and fourth-order finite difference schemes are examined for comparison. Time is discretized with the leapfrog method. The criss-cross triangle formulation is found to be unstable. The best schemes are the isosceles triangles with linear basis functions and the rectangles with bilinear basis functions.
Computers and Fluids, 14, (1986), 393–410.
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