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A nodal-based finite element approximation of the Maxwell problem suitable for singular solutions

机译:一种适用于奇异解的maxwell问题的基于节点的有限元逼近

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摘要

A new mixed finite element approximation of Maxwell’s problem is proposed, its main features being that it is based on a novel augmented formulation of the continuous problem and the introduction of a mesh\uddependent stabilizing term, which yields a very weak control on the divergence of the unknown. The method is shown to be stable and convergent in the natural H(curl; ) norm for this unknown. In particular, convergence\udalso applies to singular solutions, for which classical nodal based interpolations are known to suffer from spurious convergence upon mesh refinement.
机译:提出了麦克斯韦问题的一种新的混合有限元逼近,其主要特征是它基于对连续问题的一种新颖的增广形式,并引入了一个网格\非依赖稳定项,从而很难控制离散度。未知。对于该未知数,该方法被证明在自然H(curl;)范数中稳定且收敛。特别地,收敛\ ud也适用于奇异解,对于这些奇异解,基于经典节点的插值已知在网格细化时会出现虚假收敛。

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