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We estimate best-approximation errors using vector-valued finite elements for fields with low regularity in the scale of the fractional-order Sobolev spaces. By assuming that the target field enjoys an additional integrability property on its curl or its divergence, we establish upper bounds on these errors that can be localized to the mesh cells. These bounds are derived using the quasi-interpolation errors with or without boundary prescription derived in [A. Ern and J.-L. Guermond, ESAIM Math. Model. Numer. Anal., 51 (2017), pp. 1367–1385]. In the present work, a localized upper bound on the quasi-interpolation error is derived by using the face-to-cell lifting operators analyzed in [A. Ern and J.-L. Guermond, Found. Comput. Math., (2021)] and by exploiting the additional assumption made on the curl or the divergence of the target field. As an illustration, we show how to apply these results to the error analysis of the curl-curl problem associated with Maxwell’s equations.

In the dynamic landscape of the construction industry, the integration of computer-aided design (CAD) technology has become commonplace. However, as architectural demands evolve, so do the complexities in design and management. Consequently, Building Information Modeling (BIM) technology has emerged as a pivotal tool, progressively transforming the business landscape. This paper aims to elucidate the distinctive features and advantages of BIM technology through a comparative analysis of five key characteristics. Additionally, it delves into the practical applications of BIM in both architectural design and construction management. The foundational section of the paper illuminates the principles, concepts, and inherent characteristics of BIM technology. A comprehensive exploration of the technology's evolution in the construction industry is undertaken, highlighting its pivotal role. Subsequently, the paper offers an insightful overview of how BIM is applied in architectural design and construction management. By providing a concise analysis, this paper endeavors to instill an awareness among professionals in the construction industry about the critical aspects of information management and the unique features of BIM technology. The ultimate goal is to enhance the efficiency of architectural design and construction management practices, fostering tangible advancements in China's construction industry.