Adaptive-FEM-Based Local Coarsening Algorithm for Quadrilateral Meshes

We consider the problem of coarsening quadrilateral element meshes. As a building block of the adaptive finite element solvers, mesh coarsening is performed where the error indicator falls below a specified error bound, ensuring a high-quality solution at minimal computational cost. To achieve this goal, the mesh elements to be coarsened are selected and geometric patches are extracted from the boundary nodes of those elements. Different subregions are remeshed according to the control points along the boundary, using an appropriate meshing scale. A smoothing process is applied when necessary to preserve the original geometric boundaries of the domain. We outline a structured coarsening framework that integrates these steps into a unified algorithm. The algorithm proposed in this study make it possible to simulate a parabolic problem in time variable domains together with an arbitrary Lagrangian-Eulerian (ALE) time discretization scheme.