A New Mathematical and Computational Framework for BVPs and IVPs in Solids, Fluids, Gases and their Interactions
Abstract
During this three year time period of the grant, five major areas listed under I-V have been investigated. Summary and conclusions resulting from this research, its impact and significance have been described at the end of each section in italics. Comments and in some cases, preliminary details, are also provided for future research. In each of the five major areas of research, model problems and their numerical solutions are presented to illustrate the features of the mathematical models and their applications. Computational mathematics frame for obtaining numerical solutions of the BVPs and IVPs in these areas is based on hpk finite element method with variationally consistent integral forms in which the space or space-time local approximations are in scalar product spaces. These spaces permit higher order global differentiability local approximations that are necessary to ensure integrals over the discretizations in the Riemann sense, so that when the integrated sum of squares of the residuals approaches zero for the whole discretization we are ensured that the GDEs are satisfied in the pointwise sense. Variationally consistent integral forms (in space or space-time) yield unconditionally stable computational processes for all BVPs and IVPs.
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 04, 2015
- Accession Number
- ADA623641
Entities
People
- D. Nunez
- Junuthula N. Reddy
- K. S. Surana
Organizations
- University of Kansas