An efficient finite element computation using subparametric transformation up to cubic-order for curved triangular elements

Purpose A finite element computational methodology on a curved boundary using an efficient subparametric point transformation is presented. The proposed collocation method uses one-side curved and two-side straight triangular elements to derive exact subparametric shape functions. Design/methodology/approach Our proposed method builds upon the domain discretization into linear, quadratic and cubic-order elements using subparametric spaces and such a discretization greatly reduces the computational complexity. A unique subparametric transformation for each triangle is derived from the unique parabolic arcs via a one-of-a-kind relationship between the nodal points. Findings The novel transformation derived in this paper is shown to increase the accuracy of the finite element approximation of the boundary value problem (BVP). Our overall strategy is shown to perform well for the BVP considered in this work. The accuracy of the finite element approximate solution increases with higher-order parabolic arcs. Originality/value The proposed collocation method uses one-side curved and two-side straight triangular elements to derive exact subparametric shape functions.