Abstract
The finite element method is applied in space and time to spherically symmetric collapse in general relativity. The fluid equations are discretized with a weighted residual method in which isoparametric, bilinear approximations on quadrilaterals are used. The metric equations are constraint equations, and are approximated with cubic and linear functions on triangles. The time slices and nodal movement can be chosen arbitrarily, and a number of choices are investigated. These include a maximal slicing condition which requires an additional solution of a differential equation. The code is tested with the Riemann shock tube, and then compared with a mixed finite element/finite difference code and with a smoothed particle hydrodynamics code. Three particular simulations are used for comparisons: static, freefall collapse and collapse-and-bounce. The finite element method agrees well with the other codes, and will produce accurate results with extremely “bent” time slices.
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