| We consider the simulation of interface evolution problems in which, different length scales in the bulk and interface make for computationally challenging simulations. To address these challenges we implement (1) Newton-Schur schemes to efficiently solve coupled nonlinear equations, and (2) adaptive refinement to capture evolving interfaces.; Coupled nonlinear equations arise in various areas of computational mechanics such as: domain decomposition schemes with interior and interface degree of freedom, mixed finite elements with multiple response fields, and plasticity analyses involving displacement and material state variable fields. To solve such systems, it is common to employ nested Newton solvers that uncouple the equations. Alternatively, we employ a Newton-Schur approach and demonstrate its efficiency over the nested Newton solvers when applied to the coupled systems arising in plasticity analyses and domain decomposition.; Adaptive methods can be based on either conforming or non-conforming meshes. Though non-conforming meshes are easier to generate, they require the satisfaction of jump conditions across the non-conforming interface. In this work we develop a discontinuous Galerkin framework for such an adaptive mesh refinement. An advantage of discontinuous Galerkin schemes is that they do not introduce constraint equations and their resulting Lagrange multiplier fields as done in mixed and mortar methods. Without loss of generality we demonstrate our method by analyzing the Stefan problem of solidification. |
