WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 12, 2013
An Isoparametric Finite Element Method for Elliptic Interface Problems with Nonhomogeneous Jump Conditions
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Abstract: Numerical solutions of boundary value problems for elliptic equations with discontinuities in the coef- ficients and flux across immersed interface are of special interest. This paper develop a three order isoparametric finite element method for 2D elliptic interface problems. To obtain a high order of accuracy presents some dif- ficulty, especially if the immersed interface does not fit with the elements. For this purpose, based on an initial Cartesian mesh, a body-fitted mesh optimization strategy is proposed by introducing curved boundary elements near the interface, and a quadratic isoparametric finite element basis is constructed on the optimized mesh. Nu- merical examples with immersed interval interface demonstrate that the proposed method is efficient for elliptic interface problems with nonhomogeneous flux jump condition.
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Keywords: Isoparametric finite element, Elliptic interface problems, Curved boundary element, Body-fitted mesh, Nonhomogeneous jump conditions