We present an alternate approach based on high-order quadrature and a high-order finite element method. Both of the ingredients become possible via the use of high-order differential algebraic methods. Various examples of the method and the precision that can be achieved will be given. For example, using only about 100 finite elements of order 7, accuracies in the range of 10-6 can be obtained in the 3D case.
S. Manikonda, M. Berz, International Journal of Pure and Applied Mathematics 23,3 (2005) 365-378
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