,A ROBUST FINITE ELEMENT METHOD FOR A 3-D ELLIPTIC SINGULAR PERTURBATION PROBLEM

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This paper proposes a robust finite element method for a three-dimensional fourth-order elliptic singular perturbation problem. The method uses the three-dimensional Morley element and replaces the finite element functions in the part of bilinear form corresponding to the second-order differential operator by a suitable approximation. To give such an approximation, a convergent nonconforming element for the second-order problem is constructed.It is shown that the method converges uniformly in the perturbation parameter.
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