Huo-Yuan Duan

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This paper provides a new strict mathematical analysis for the velocity-pressurevorticity least-squares methods (i.e., the standard linear element method and the Bochev–Gunzburger method) for the 3D Stokes problem with homogeneous velocity boundary condition. The analysis shows that, in general, the divergence of the vorticity does not affect the(More)
More than a decade ago, Bramble, Pasciak and Xu developed a framework in analyzing the multigrid methods with nonnested spaces or noninherited quadratic forms. It was subsequently known as the BPX multigrid framework, which was widely used in the analysis of multigrid and domain decomposition methods. However, the framework has an apparent limit in the(More)
Abstract. To deal with the divergence-free constraint in a double curl problem: curlμ−1curlu = f and div εu = 0 in Ω, where μ and ε represent the physical properties of the materials occupying Ω, we develop a δ-regularization method: curlμcurluδ + δεuδ = f to completely ignore the divergence-free constraint div εu = 0. It is shown that uδ converges to u in(More)
In this paper we analyze the finite element discretization for the first-order system least squares mixed model for the second-order elliptic problem by means of using nonconforming and conforming elements to approximate displacement and stress, respectively. Moreover, on arbitrary regular quadrilaterals, we propose new variants of both the rotated Q1(More)
In this paper we develop the C0 finite element method for a generalized curlcurl-grad div indefinite Maxwell problem in a Lipschitz domain such as nonconvex polygon for which the solution of the problem may be nonsmooth and only have the Hr regularity for some r < 1. The ingredients of our method are that two ‘mass-lumping’ L2 projectors are applied to curl(More)
More than a decade ago, Bramble, Pasciak and Xu developed a framework in analyzing the multigrid methods with nonnested spaces or noninherited quadratic forms. It was subsequently known as the BPX multigrid framework, which was widely used in the analysis of multigrid and domain decomposition methods. However, the framework has an apparent limit in the(More)