Adaptive Higher-Order Methods for Problems in Elastodynamics

Abstract

This document summarizes results obtained on a project aimed at developing new classes of numerical methods for the analysis of problems in elastodynamics and elastostatics. Two significant classes of new methods were developed, analyzed, and implemented: 1) the so-called hp-Cloud Method, a variant of the meshfree methods built on partitions of unity generated by traditional finite elements (also referred to as the Generalized Finite Element Method GFEM) and, 2) Discontinuous Galerkin Methods for broad classes of transport problems, including problems with significant diffusion. These new methods offer numerous advantages over traditional schemes for a significant class of applications. A summary of major features is given together with an Appendix outlining a priori error estimates and convergence proofs for various Discontinuous Galerkin Methods.

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 2000
Accession Number
ADA389478

Entities

People

  • J. Tinsley Oden

Tags

Communities of Interest

  • C4I
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Applied Mechanics
  • Boundary Layer
  • Boundary Value Problems
  • Computational Fluid Dynamics
  • Computational Science
  • Differential Equations
  • Equations
  • Euler Equations
  • Finite Element Analysis
  • Fluid Dynamics
  • Fluid Mechanics
  • Galerkin Method
  • Mathematical Analysis
  • Mathematics
  • Navier Stokes Equations
  • Numerical Analysis
  • Numerical Methods And Procedures

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Systems Analysis and Design