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This paper proposes a strategy to solve the problems of the conventionals-version of finite element method (SFEM) fundamentally. Because SFEM canreasonably model an analytical domain by superimposing meshes with differentspatial resolutions, it has intrinsic advantages of local high accuracy, lowcomputation time, and simple meshing procedure. However, it has disadvantagessuch as accuracy of numerical integration and matrix singularity. Althoughseveral additional techniques have been proposed to mitigate these limitations,they are computationally expensive or ad-hoc, and detract from its strengths.To solve these issues, we propose a novel strategy called B-spline based SFEM.To improve the accuracy of numerical integration, we employed cubic B-splinebasis functions with $C^2$-continuity across element boundaries as the globalbasis functions. To avoid matrix singularity, we applied different basisfunctions to different meshes. Specifically, we employed the Lagrange basisfunctions as local basis functions. The numerical results indicate that usingthe proposed method, numerical integration can be calculated with sufficientaccuracy without any additional techniques used in conventional SFEM.Furthermore, the proposed method avoids matrix singularity and is superior toconventional methods in terms of convergence for solving linear equations.Therefore, the proposed method has the potential to reduce computation timewhile maintaining a comparable accuracy to conventional SFEM.

Higher-continuity s-version of finite element method with B-spline functions