Combining Size-Preserving and Smoothing Procedures for Adaptive Quadrilateral Mesh Generation

It is well known that the variations of the element size have to be controlled in order to generate a high-quality mesh. Hence, several techniques have been developed to limit the gradient of the element size. However, the obtained discretizations do not always reproduce the prescribed size function. This is of the major importance for quadrilateral meshes, since they are much more constrained than triangular ones. To solve this issue, we first define a quantitative criterion to assess when an element reproduces the prescribed size function. Then, using this criterion, we develop the novel size-preserving technique to create a new size function that ensures a high-quality mesh where all the elements are of the correct size. Two direct applications are presented. First, the size-preserving approach allows to generate quadrilateral meshes that correctly preserve the prescribed element size, without coarsen or refine the mesh. Second, we show that we can reduce the number of iterations to converge an adaptive process, since we do not need additional iterations to generate a mesh that correctly reproduces the size function. A smoother is applied in order to further increase the element quality while preserving the element size. Only when combining the size-preserving technique and the smoother, a high-quality mesh that correctly reproduces the size function is obtained.