A moving mesh framework based on three parametrization layers for 1d PDEs

Solutions of partial differential equations (PDEs) arising in science and industrial applications often undergo large variations occurring over small parts of the domain. Resolving steep gradients and oscillations properly is a numerical challenge. The idea of the r-refinement (moving mesh) is to improve the approximation quality-while keeping the computational effort-by redistributing a fixed number of grid points in areas of the domain where they are needed. In this work we develop a general moving mesh framework for 1d PDEs that is based on three parameterization layers representing referential, computational and desired parameters. Numerical results are shown for two different strategies that are applied to a fiber spinning process.