The prospective generalised MATLAB 2D mesh generation codes, HOmesh2d for the regular domain and CurvedHOmesh2d for a circular domain are based on the MATLAB mesh generator distmesh of Persson and Strang. This approach is shown to drastically simplify the computational complexities involved in the HO finite element (HOFE) formulation of any partial differential equation (PDE). The proposed HO scheme uses the nodal relations obtained from subparametric transformations with parabolic arcs, especially for curved geometry. This paper presents a novel automated higher-order (HO) unstructured triangular mesh generation of the two-dimensional domain. It is shown that coarse HO meshes of 21 and 28-noded triangle elements outperform the fine linear and quadratic meshes in terms of the accuracy of the numerical results as well as degrees of freedom and number of elements are reduced in the FEA. Numerical examples show the simplicity, efficiency and accuracy of HOFE scheme with the proposed HO automated mesh generation techniques up to 28- noded triangle elements (sextic triangular elements). The proposed approach drastically simplifies the computational complexities involved in the FE formulation and thus increasing the efficiency of the HOFE scheme.
Illustrated HO finite element (HOFE) method for some elliptic PDE using the proposed technique.
The interior nodes and nodes on the boundaries are obtained using subparametric transformations with parabolic arcs especially for curved geometries. A novel higher order (HO) automated unstructured triangular mesh generation is presented with the MATLAB code for regular and curved geometries.
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