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A new finite element (FE) scheme, based on the decomposition of a second order differential equation into a set of first order symplectic (Hamiltonian) equations, is presented and tested on a one-dimensional, driven Sturm-Liouville problem. Error analysis shows improved cubic convergence in the energy norm for piecewise linear "tent" elements, as compared to quadratic convergence for the standard and symplectic hybrid (i.e. ôtentö and piecewise constant) FE methods. The convergence deteriorates in the presence of a regular singular point, but can be recovered by appropriate mesh node packing. Optimal mesh packing exponents are derived to ensure cubic (respectively quadratic for the hybrid FE method) convergence with minimal numerical error. The symplectic hybrid FE scheme is shown to be approximately 30-40 times more accurate than the standard FE scheme, for an exact test problem based on determining the non-ideal magnetohydrodynamic stability of a fusion plasma. A further suppression of the error by one order of magnitude is achieved for the symplectic tent element method.

Additional information

Authors: PLETZER A, Centre de Recherches en Physique des Plasmas, EURATOM Association-Confederation Suisse, Ecole Polytechnique Federale de Lausanne (CH)
Bibliographic Reference: An article published in: Elsevier Computer Physics Communications 96 (1996) pp.1-9
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