Convergence analysis of finite element methods for H (curl; Ω)-elliptic interface problems

In this article we investigate the analysis of a finite element method for solving H(curl; Ω)-elliptic interface problems in general three-dimensional polyhedral domains with smooth interfaces. The continuous problems are discretized by means of the first family of lowest order Nédélec H(curl; Ω)-conforming finite elements on a family of tetrahedral meshes which resolve the smooth interface in the sense of sufficient approximation in terms of a parameter δ that quantifies the mismatch between the smooth interface and the triangulation. Optimal error estimates in the H(curl; Ω)-norm are obtained for the first time. The analysis is based on a δ-strip argument, a new extension theorem for H 1(curl; Ω)-functions across smooth interfaces, a novel non-standard interface-aware interpolation operator, and a perturbation argument for degrees of freedom for H(curl; Ω)-conforming finite elements. Numerical tests are presented to verify the theoretical predictions and confirm the optimal order convergence of the numerical solutio

Real interpolation of spaces of differential forms

In this paper, we study interpolation of Hilbert spaces of differential forms using the real method of interpolation. We show that the scale of fractional order Sobolev spaces of differential l-forms in H s with exterior derivative in H s can be obtained by real interpolation. Our proof heavily relies on the recent discovery of smoothed Poincaré lifting for differential forms [M. Costabel and A. McIntosh, On Bogovskii and regularized Poincare integral operators for de Rham complexes on Lipschitz domains, Math. Z. 265(2): 297-320, 2010]. They enable the construction of universal extension operators for Sobolev spaces of differential forms, which, in turns, pave the way for a Fourier transform based proof of equivalences of K-functional

Convergence analysis of finite element methods for H(curl; Omega)-elliptic interface problems

ISSN:0029-599XISSN:0945-324

Relationship among self‐injury, experiential avoidance, cognitive fusion, anxiety, and depression in Chinese adolescent patients with nonsuicidal self‐injury

Abstract Objective To explore relationship among self‐injury behavior, experiential avoidance, cognitive fusion, anxiety, and depression in Chinese adolescent patients with nonsuicidal self‐injury (NSSI). Methods Cognitive fusion questionnaire (CFQ), Acceptance and Action Questionnaire—2nd edition (AAQ‐II), adolescent nonsuicidal self‐injury behavior questionnaire (ANSAQ), Hamilton Anxiety Scale (HAMA), and Hamilton Depression Scale (HAMD) were used as research tools to investigate 120 subjects with NSSI and 130 healthy controls. Results The scores of CFQ and AAQ‐II in the NSSI group were significantly higher than those in the healthy control group (p < .001). The results of regression analysis showed that the experiential avoidance score of patients with NSSI could predict the score of self‐injury questionnaire (β = 0.585, p < .001); when predicting anxiety, only CFQ (β = 0.361, p < .001) entered the equation, with an explanatory variation of 12.3%; when predicting depression, CFQ (β = 0.287, p < .01) entered the equation, with an explanatory variation of 7.4%. Conclusion A high level of cognitive fusion and experiential avoidance may be important factors for the maintenance of self‐injury behavior in patients with NSSI