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Two robust nonconforming H$^2-$elements for linear strain gradient elasticity

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arxiv 1604.02187 v2 pith:GE76AYAJ submitted 2016-04-07 math.NA cs.NA

classification math.NAcs.NA
keywords elementsnonconformingelasticitygradientperturbationstrainapproximatearising
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abstract

We propose two nonconforming finite elements to approximate a boundary value problem arising from strain gradient elasticity, which is a higher-order perturbation of the linearized elastic system. Our elements are H$^2-$nonconforming while H$^1-$conforming. We show both elements converges in the energy norm uniformly with respect to the perturbation parameter.

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