Adaptive Mesh Mapping for Partial Differential Equations

We present mesh mapping techniques for transient nonlinear partial differential equations in one space dimension. For a fixed time t, our approach is based on mapping the solution u(x,t) into an alternative spatial coordinate system ^ over u(xi,t) = u(x(xi),t). If u and x are written in terms of B-splines, then the x mapping may be constructed using free knot placement techniques, such as deBoor's NEWNOT approach.