A refinement of unstructured quadrilateral and mixed meshes

This paper studies the refinement of unstructured quadrilateral and mixed meshes. We propose the variations for the definition of refinement templates “in nine cells” for the case if there is an unstructured quadrilateral mesh, which ensures cell's convexity of the result mesh. To control the maximum permissible mesh angle, we use the templates of refining the cells of bad quality. In addition, this paper presents a new unstructured mixed mesh refinement algorithm; also, we give several demonstration examples of the algorithm that show the considerable improvement of mesh quality, as compared with the well-known methods.