Size preserving mesh generation in adaptivity processes

Abstract

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. Although these methods allow generating high-quality meshes, the obtained discretizations do not always reproduce the prescribed size function. Specifically, small elements may not be generated in a region where small element size is prescribed. This is critical for many practical simulations, where small elements are needed to reduce the error of the numerical simulation. To solve this issue, we present the novel size-preserving technique to control the mesh size function prescribed at the vertices of a background mesh. The result is a new size function that ensures a high-quality mesh with all the elements smaller or equal to the prescribed element size. That is, we ensure that the new mesh handles at least one element of the correct size at each local minima of the size function. In addition, the gradient of the size function is limited to obtain a high-quality mesh. Two direct applications are presented. First, 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 valid mesh. Second, the size-preserving approach allows to generate quadri- lateral meshes that correctly preserves the prescribed element size.Peer ReviewedPostprint (published version