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BIBLIOGRAPHY INDEX CONTENTS ix 427 517 545 PREFACE This book treats parts of the mathematical foundations of three-dimensional elasticity using modern differential geometry and functional analysis. It is intended for mathematicians, engineers, and physicists who wish to s~e this classical subject in a modern setting and to see some examples of what newer(More)
The variational multiscale method is applied to the large eddy simulation ͑LES͒ of homogeneous, isotropic flows and compared with the classical Smagorinsky model, the dynamic Smagorinsky model, and direct numerical simulation ͑DNS͒ data. Overall, the multiscale method is in better agreement with the DNS data than both the Smagorinsky model and the dynamic(More)
We derive an explicit formula for the fine-scale Green's function arising in variational mul-tiscale analysis. The formula is expressed in terms of the classical Green's function and a projector which defines the decomposition of the solution into coarse and fine scales. The theory is presented in an abstract operator format and subsequently specialized for(More)
We consider a family of mixed finite element discretizations of the Darcy flow equations using totally discontinuous elements (both for the pressure and the flux variable). Instead of using a jump stabilization as it is usually done for DG methods (see e.g. [3], [13] and the references therein) we use the stabilization introduced in [18], [17]. We show that(More)
A new mixed, stabilized, discontinuous Galerkin formulation for Darcy flow is presented. The formulation combines several attributes not simultaneously satisfied by other methods: It is convergent for any combination of velocity and pressure interpolation higher than first-order, it exactly satisfies a mass balance on each element, and it passes two-and(More)
This paper describes an automatic and efficient approach to construct unstructured tetrahedral and hexahedral meshes for a composite domain made up of heterogeneous materials. The boundaries of these material regions form non-manifold surfaces. In earlier papers, we developed an octree-based isocontouring method to construct unstructured 3D meshes for a(More)
Proliferation of degrees-of-freedom has plagued discontinuous Galerkin methodology from its inception over 30 years ago. This paper develops a new computational formulation that combines the advantages of discontinuous Galerkin methods with the data structure of their continuous Galerkin counterparts. The new method uses local, element wise problems to(More)
  • Ii Iii, J Tinsley Oden, Ted Belytschko, Walter P Murphy, Mccormick Professor, Jacob Fish +39 others
  • 2006
ix PREFACE This document is the final report of the findings and recommendations of the Blue Ribbon Panel on Simulation-Based Engineering Science. The report contains recommendations critical to the acceleration of advances in Simulation-Based Engineering Science (SBES), and it identifies several areas in which SBES can play a remarkable role in promoting(More)
We study a multiscale discontinuous Galerkin method introduced in [10] that reduces the computational complexity of the discontinuous Galerkin method, seemingly without adversely affecting the quality of results. For a stabilized variant we are able to obtain the same error estimates for the advection-diffusion equation as for the usual discontinuous(More)