Rediscretizations, moving meshes and solution mapping in h, p, k framework for BVPs and IVPs

Rediscretization, moving mesh and solution mapping approaches are presented for boundary value problems (BVPs) and initial value problems (IVPs). When BVPs are solved using mathematical models in Lagrangian frame of reference, the discretizations often become excessively distorted during load incrementing. Rediscretization and a total map of the solution from the original discretization is beneficial in such cases. In the case of IVPs, using space-time strips with time marching, the moving mesh approach permits accurate evolutions of high solution gradient moving fronts using computationally practical spatial discretizations. Both the rediscretization and moving mesh procedure require mapping of the geometry of the new discretization (whole or part of the boundary) onto the original discretization and then mapping of the solution using this geometry map.; Rediscretization and moving mesh approaches for 1D and 2D cases are considered for local approximation of C0,C 0,0 Lagrange type, C0,C 0,0 p-version hierarchical as well as C i,Ci,j approximations of higher order global differentiability. Merits of higher order global differentiability approximations in h, p, k mathematical and computational framework are demonstrated for rediscretizations as well as moving meshes. Inter-element flux problems present in currently used procedures are examined for C0 local approximations. Remedies are presented and their absence is clearly shown when the local approximations are of higher classes than C0. Introduction, literature review and scope of work is presented in Chapter 1. Chapter 2 contains developments of methodologies, approaches and procedures. Numerical studies are presented in Chapter 3. Summary and conclusions are given in Chapter 4.