查看更多>>摘要：For singularly perturbed convection-diffusion problems,supercloseness analysis of the finite element method is still open on Bakhvalov-type meshes,especially in the case of 2D.The difficulties arise from the width of the mesh in the layer adjacent to the transition point,resulting in a suboptimal estimate for convergence.Existing analysis techniques cannot handle these difficulties well.To fill this gap,here a novel interpolation is designed delicately for the smooth part of the solution,bringing about the optimal supercloseness result of almost order 2 under an energy norm for the finite element method.Our theoretical result is uniform in the singular perturbation parameter ε and is supported by the numerical experiments.
查看更多>>摘要：For each real number x ∈(0,1),let[a1(x),a2(x),…,an(x),…]denote its con-tinued fraction expansion.We study the convergence exponent defined byτ(x):=inf{s≥ 0:∞Σn=1(an(x)an+1(x))-s＜∞},which reflects the growth rate of the product of two consecutive partial quotients.As a main result,the Hausdorff dimensions of the level sets of r(x)are determined.
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