Accession Number : ADA131824

Title :   Adaptive Finite Element Methods for Parabolic Partial Differential Equations.

Descriptive Note : Interim rept.,

Corporate Author : RENSSELAER POLYTECHNIC INST TROY NY DEPT OF MATHEMATICAL SCIENCES

Personal Author(s) : Flaherty,Joseph E ; Coyle,J Michael ; Ludwig,Raymond ; Davis,Stephen F

PDF Url : ADA131824

Report Date : May 1983

Pagination or Media Count : 23

Abstract : The authors discuss a finite element method for solving initial-boundary value problems for vector systems of partial differential equations in one space dimension and time. The method automatically adjusts the computational mesh as the solution evolves in time so as to approximately minimize the local discretization error. They are thus able to calculate accurate solutions with fewer elements than would be necessary with a uniform mesh. This overall method contains two distinct steps: a solution step and a mesh selection step. They solve the partial differential equations using a finite element-Galerkin method on trapezoidal space-time-elements with either piecewise linear or cubic Hermits polynomial approximations. A variety of mesh selection strategies are discussed and analyzed. Results are presented for several computational examples.

Descriptors :   *Finite element analysis, *Partial differential equations, *Boundary value problems, Problem solving, Vector analysis, Computations, Mesh, Algorithms, Solutions(General)

Subject Categories : Theoretical Mathematics
      Fluid Mechanics

Distribution Statement : APPROVED FOR PUBLIC RELEASE