Local defect correction in numerical simulation of surface remelting

We study the efficient numerical simulation of laser surface remelting, a process to improve the surface quality of steel components. To this end we use adaptive grids, which are well-suited for problems with moving heat sources. To account for the local high activity due to the heat source, we introduce local uniform grids and couple the solutions on the global coarse and local fine grids using local defect correction (LDC). LDC is based on simple data structures and simple discretization stencils on uniform or tensor-product grids