Adaptive Higher-Order Methods for Problems in Elastodynamics

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...

Full description

Saved in:
Bibliographic Details
Main Author: Oden, J Tinsley
Format: Report
Language:English
Subjects:
Acoustics
BOUNDARY VALUE PROBLEMS
DGM(DISCONTINUOUS GALERKIN METHODS)
ELASTIC WAVES
ELASTODYNAMICS
ELASTOSTATICS
FINITE ELEMENT ANALYSIS
GALERKIN METHOD
GFEM(GENERALIZED FINITE ELEMENT METHOD)
HP-CLOUD METHOD
Numerical Mathematics
PUM(PARTITION OF UNITY METHODS)
Theoretical Mathematics
Online Access:Request full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.