Download or read book On Discontinuous Galerkin Methods for Singularly Perturbed and Incompressible Miscible Displacement Problems written by John Robert Chapman and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis is concerned with the numerical approximation of problems of fluid flow, in particular the stationary advection diffusion reaction equations and the time dependent, coupled equations of incompressible miscible displacement in a porous medium. We begin by introducing the continuous discontinuous Galerkin method for the singularly perturbed advection diffusion reaction problem. This is a method which coincides with the continuous Galerkin method away from internal and boundary layers and with a discontinuous Galerkin method in the vicinity of layers. We prove that this consistent method is stable in the streamline diffusion norm if the convection field flows non-characteristically from the region of the continuous Galerkin to the region of the discontinuous Galerkin method. We then turn our attention to the equations of incompressible miscible displacement for the concentration, pressure and velocity of one fluid in a porous medium being displaced by another. We show a reliable a posteriori error estimator for the time dependent, coupled equations in the case where the solution has sufficient regularity and the velocity is bounded. We remark that these conditions may not be attained in physically realistic geometries. We therefore present an abstract approach to the stationary problem of miscible displacement and investigate an a posteriori error estimator using weighted spaces that relies on lower regularity requirements for the true solution. We then return to the continuous discontinuous Galerkin method. We prove in an abstract setting that standard (continuous) Galerkin finite element approximations are the limit of interior penalty discontinuous Galerkin approximations as the penalty parameter tends to infinity. We then show that by varying the penalization parameter on only a subset of the domain we reach the continuous discontinuous method in the limit. We present numerical experiments illustrating this approach both for equations of non-negative characteristic form (closely related to advection diffusion reaction equations) and to the problem of incompressible miscible displacement. We show that we may practically determine appropriate discontinuous and continuous regions, resulting in a significant reduction of the number of degrees of freedom required to approximate a solution, by using the properties of the discontinuous Galerkin approximation to the advection diffusion reaction equation. We finally present novel code for implementing the continuous discontinuous Galerkin method in C++.
Download or read book Discontinuous Galerkin Method written by Vít Dolejší and published by Springer. This book was released on 2015-07-17 with total page 575 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of the book is the mathematical theory of the discontinuous Galerkin method (DGM), which is a relatively new technique for the numerical solution of partial differential equations. The book is concerned with the DGM developed for elliptic and parabolic equations and its applications to the numerical simulation of compressible flow. It deals with the theoretical as well as practical aspects of the DGM and treats the basic concepts and ideas of the DGM, as well as the latest significant findings and achievements in this area. The main benefit for readers and the book’s uniqueness lie in the fact that it is sufficiently detailed, extensive and mathematically precise, while at the same time providing a comprehensible guide through a wide spectrum of discontinuous Galerkin techniques and a survey of the latest efficient, accurate and robust discontinuous Galerkin schemes for the solution of compressible flow.
Download or read book Numerical Mathematics and Advanced Applications 2011 written by Andrea Cangiani and published by Springer Science & Business Media. This book was released on 2013-01-20 with total page 811 pages. Available in PDF, EPUB and Kindle. Book excerpt: The European Conferences on Numerical Mathematics and Advanced Applications (ENUMATH) are a series of conferences held every two years to provide a forum for discussion of new trends in numerical mathematics and challenging scientific and industrial applications at the highest level of international expertise. ENUMATH 2011 was hosted by the University of Leicester (UK) from the 5th to 9th September 2011. This proceedings volume contains more than 90 papers by speakers of the conference and gives an overview of recent developments in scientific computing, numerical analysis, and practical use of modern numerical techniques and algorithms in various applications. New results on finite element methods, multiscale methods, numerical linear algebra, and finite difference schemes are presented. A range of applications include computational problems from fluid dynamics, materials, image processing, and molecular dynamics.
Download or read book Nodal Discontinuous Galerkin Methods written by Jan S. Hesthaven and published by Springer Science & Business Media. This book was released on 2007-12-20 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an introduction to the key ideas, basic analysis, and efficient implementation of discontinuous Galerkin finite element methods (DG-FEM) for the solution of partial differential equations. It covers all key theoretical results, including an overview of relevant results from approximation theory, convergence theory for numerical PDE’s, and orthogonal polynomials. Through embedded Matlab codes, coverage discusses and implements the algorithms for a number of classic systems of PDE’s: Maxwell’s equations, Euler equations, incompressible Navier-Stokes equations, and Poisson- and Helmholtz equations.
Download or read book Analysis of Hybrid Discontinuous Galerkin Methods for Incompressible Flow Problems written by Christian Waluga and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Local Discontinuous Galerkin Methods for Partial Differential Equations with Higher Order Derivatives written by National Aeronautics and Space Adm Nasa and published by . This book was released on 2018-09-27 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we review the existing and develop new continuous Galerkin methods for solving time dependent partial differential equations with higher order derivatives in one and multiple space dimensions. We review local discontinuous Galerkin methods for convection diffusion equations involving second derivatives and for KdV type equations involving third derivatives. We then develop new local discontinuous Galerkin methods for the time dependent bi-harmonic type equations involving fourth derivatives, and partial differential equations involving fifth derivatives. For these new methods we present correct interface numerical fluxes and prove L(exp 2) stability for general nonlinear problems. Preliminary numerical examples are shown to illustrate these methods. Finally, we present new results on a post-processing technique, originally designed for methods with good negative-order error estimates, on the local discontinuous Galerkin methods applied to equations with higher derivatives. Numerical experiments show that this technique works as well for the new higher derivative cases, in effectively doubling the rate of convergence with negligible additional computational cost, for linear as well as some nonlinear problems, with a local uniform mesh. Yan, Jue and Shu, Chi-Wang and Bushnell, Dennis M. (Technical Monitor) Langley Research Center NASA/CR-2002-211959, NAS 1.26:211959, ICASE-2002-42...
Download or read book Adaptive Discontinuous Galerkin Methods for Fourth Order Problems written by Juha Mikael Virtanen and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is concerned with the derivation of adaptive methods for discontinuous Galerkin approximations of linear fourth order elliptic and parabolic partial differential equations. Adaptive methods are usually based on a posteriori error estimates. To this end, a new residual-based a posteriori error estimator for discontinuous Galerkin approximations to the biharmonic equation with essential boundary conditions is presented. The estimator is shown to be both reliable and efficient with respect to the approximation error measured in terms of a natural energy norm, under minimal regularity assumptions. The reliability bound is based on a new recovery operator, which maps discontinuous finite element spaces to conforming finite element spaces (of two polynomial degrees higher), consisting of triangular or quadrilateral Hsieh-Clough-Tocher macroelements. The efficiency bound is based on bubble function techniques. The performance of the estimator within an h-adaptive mesh refinement procedure is validated through a series of numerical examples, verifying also its asymptotic exactness. Some remarks on the question of proof of convergence of adaptive algorithms for discontinuous Galerkin for fourth order elliptic problems are also presented. Furthermore, we derive a new energy-norm a posteriori error bound for an implicit Euler time-stepping method combined with spatial discontinuous Galerkin scheme for linear fourth order parabolic problems. A key tool in the analysis is the elliptic reconstruction technique. A new challenge, compared to the case of conforming finite element methods for parabolic problems, is the control of the evolution of the error due to non-conformity. Based on the error estimators, we derive an adaptive numerical method and discuss its practical implementation and illustrate its performance in a series of numerical experiments.
Download or read book Mathematical Reviews written by and published by . This book was released on 2005 with total page 1852 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1979 with total page 1096 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Discontinuous Galerkin Methods written by Bernardo Cockburn and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: A class of finite element methods, the Discontinuous Galerkin Methods (DGM), has been under rapid development recently and has found its use very quickly in such diverse applications as aeroacoustics, semi-conductor device simula tion, turbomachinery, turbulent flows, materials processing, MHD and plasma simulations, and image processing. While there has been a lot of interest from mathematicians, physicists and engineers in DGM, only scattered information is available and there has been no prior effort in organizing and publishing the existing volume of knowledge on this subject. In May 24-26, 1999 we organized in Newport (Rhode Island, USA), the first international symposium on DGM with equal emphasis on the theory, numerical implementation, and applications. Eighteen invited speakers, lead ers in the field, and thirty-two contributors presented various aspects and addressed open issues on DGM. In this volume we include forty-nine papers presented in the Symposium as well as a survey paper written by the organiz ers. All papers were peer-reviewed. A summary of these papers is included in the survey paper, which also provides a historical perspective of the evolution of DGM and its relation to other numerical methods. We hope this volume will become a major reference in this topic. It is intended for students and researchers who work in theory and application of numerical solution of convection dominated partial differential equations. The papers were written with the assumption that the reader has some knowledge of classical finite elements and finite volume methods.
Download or read book The Mathematics of Reservoir Simulation written by Richard E. Ewing and published by SIAM. This book was released on 2014-12-01 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the state of the art of the mathematical theory and numerical analysis of imaging. Some of the applications covered in the book include computerized tomography, magnetic resonance imaging, emission tomography, electron microscopy, ultrasound transmission tomography, industrial tomography, seismic tomography, impedance tomography, and NIR imaging.
Download or read book Numerical Solution of Two Point Boundary Value Problems written by Herbert B. Keller and published by SIAM. This book was released on 1976-01-01 with total page 69 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lectures on a unified theory of and practical procedures for the numerical solution of very general classes of linear and nonlinear two point boundary-value problems.
Download or read book Fluid Mechanics written by L D Landau and published by Elsevier. This book was released on 2013-09-03 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fluid Mechanics, Second Edition deals with fluid mechanics, that is, the theory of the motion of liquids and gases. Topics covered range from ideal fluids and viscous fluids to turbulence, boundary layers, thermal conduction, and diffusion. Surface phenomena, sound, and shock waves are also discussed, along with gas flow, combustion, superfluids, and relativistic fluid dynamics. This book is comprised of 16 chapters and begins with an overview of the fundamental equations of fluid dynamics, including Euler's equation and Bernoulli's equation. The reader is then introduced to the equations of motion of a viscous fluid; energy dissipation in an incompressible fluid; damping of gravity waves; and the mechanism whereby turbulence occurs. The following chapters explore the laminar boundary layer; thermal conduction in fluids; dynamics of diffusion of a mixture of fluids; and the phenomena that occur near the surface separating two continuous media. The energy and momentum of sound waves; the direction of variation of quantities in a shock wave; one- and two-dimensional gas flow; and the intersection of surfaces of discontinuity are also also considered. This monograph will be of interest to theoretical physicists.
Download or read book Domain Decomposition Methods Algorithms and Theory written by Andrea Toselli and published by Springer Science & Business Media. This book was released on 2006-06-20 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a comprehensive presentation of some of the most successful and popular domain decomposition preconditioners for finite and spectral element approximations of partial differential equations. It places strong emphasis on both algorithmic and mathematical aspects. It covers in detail important methods such as FETI and balancing Neumann-Neumann methods and algorithms for spectral element methods.
Download or read book Models of Phase Transitions written by Augusto Visintin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: ... "What do you call work?" "Why ain't that work?" Tom resumed his whitewashing, and answered carelessly: "Well. lI1a), he it is, and maybe it aill't. All I know, is, it suits Tom Sawvc/:" "Oil CO/lll!, IIOW, Will do not mean to let 011 that you like it?" The brush continued to move. "Likc it? Well, I do not see wlzy I oughtn't to like it. Does a hoy get a chance to whitewash a fence every day?" That put the thing ill a Ilew light. Ben stopped nibhling the apple ... (From Mark Twain's Adventures of Tom Sawyer, Chapter II.) Mathematics can put quantitative phenomena in a new light; in turn applications may provide a vivid support for mathematical concepts. This volume illustrates some aspects of the mathematical treatment of phase transitions, namely, the classical Stefan problem and its generalizations. The in tended reader is a researcher in application-oriented mathematics. An effort has been made to make a part of the book accessible to beginners, as well as physicists and engineers with a mathematical background. Some room has also been devoted to illustrate analytical tools. This volume deals with research I initiated when I was affiliated with the Istituto di Analisi Numerica del C.N.R. in Pavia, and then continued at the Dipartimento di Matematica dell'Universita di Trento. It was typeset by the author in plain TEX
Download or read book Rheological Fundamentals of Polymer Processing written by J.A. Covas and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: Experts in rheology and polymer processing present up-to-date, fundamental and applied information on the rheological properties of polymers, in particular those relevant to processing, contributing to the physical understanding and the mathematical modelling of polymer processing sequences. Basic concepts of non-Newtonian fluid mechanics, micro-rheological modelling and constitutive modelling are reviewed, and rheological measurements are described. Topics with practical relevance are debated, such as linear viscoelasticity, converging and diverging flows, and the rheology of multiphase systems. Approximation methods are discussed for the computer modelling of polymer melt flow. Subsequently, polymer processing technologies are studied from both simulation and engineering perspectives. Mixing, crystallization and reactive processing aspects are also included. Audience: An integrated and complete view of polymer processing and rheology, important to institutions and individuals engaged in the characterisation, testing, compounding, modification and processing of polymeric materials. Can also support academic polymer processing engineering programs.
Download or read book FEFLOW written by Hans-Jörg G. Diersch and published by Springer Science & Business Media. This book was released on 2013-11-22 with total page 1018 pages. Available in PDF, EPUB and Kindle. Book excerpt: FEFLOW is an acronym of Finite Element subsurface FLOW simulation system and solves the governing flow, mass and heat transport equations in porous and fractured media by a multidimensional finite element method for complex geometric and parametric situations including variable fluid density, variable saturation, free surface(s), multispecies reaction kinetics, non-isothermal flow and multidiffusive effects. FEFLOW comprises theoretical work, modeling experiences and simulation practice from a period of about 40 years. In this light, the main objective of the present book is to share this achieved level of modeling with all required details of the physical and numerical background with the reader. The book is intended to put advanced theoretical and numerical methods into the hands of modeling practitioners and scientists. It starts with a more general theory for all relevant flow and transport phenomena on the basis of the continuum approach, systematically develops the basic framework for important classes of problems (e.g., multiphase/multispecies non-isothermal flow and transport phenomena, discrete features, aquifer-averaged equations, geothermal processes), introduces finite-element techniques for solving the basic balance equations, in detail discusses advanced numerical algorithms for the resulting nonlinear and linear problems and completes with a number of benchmarks, applications and exercises to illustrate the different types of problems and ways to tackle them successfully (e.g., flow and seepage problems, unsaturated-saturated flow, advective-diffusion transport, saltwater intrusion, geothermal and thermohaline flow).
