In the proposed work we consider a geometrically based method for modeling and analysis of problems governed by partial differential equations such as, for example, solids, structures and fluids. Basis functions generated from underlying expo-rational basis blended with local geometry are employed to model a finite element mesh. The same basis functions are used for the analysis without changing the geometry or its parameterization.

Strictly local basis functions make the proposed method closer to a basic finite element method, while the adjustable continuity between elements provides a link with meshless methods. In the context of structural mechanics, these basis functions smoothly represent elastic deformations.

We demonstrate computational and algorithmic efficiency of spline-based elements for the analysis purpose. Blending spline type constructions generalizing standard modeling techniques yield flexible and adaptive geometry.