Download or read book Adaptive Multilevel Discretization in Time and Space for Parabolic Partial Differential Equations written by Folkmar A. Bornemann and published by . This book was released on 1989 with total page 75 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite element approximation then leads to perturbed expansions, whose perturbations, however, can be pushed below a necessary level by means of an adaptive grid control. The arising space grids are not required to satisfy any quasi- uniformity assumption. Even though the theoretical presentation is independent of space dimension details of the algorithm and numerical examples are given for the 1-D case only. For the 1-D elliptic solver, which is used, an error estimator is established, which works uniformly well for a family of elliptic problems. The numerical results clearly show the significant perspectives opended [sic] by the new algorithmic approach."
Download or read book Adaptive Multilevel Discretization in Time and Space for Parabolic Partial Differential Equations written by Folkmar A. Bornemann and published by . This book was released on 1989 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite element approximation then leads to perturbed expansions, whose perturbations, however, can be pushed below a necessary level by means of an adaptive grid control. The arising space grids are not required to satisfy any quasi- uniformity assumption. Even though the theoretical presentation is independent of space dimension details of the algorithm and numerical examples are given for the 1-D case only. For the 1-D elliptic solver, which is used, an error estimator is established, which works uniformly well for a family of elliptic problems. The numerical results clearly show the significant perspectives opended [sic] by the new algorithmic approach."
Download or read book Adaptive Multilevel Solution of Nonlinear Parabolic PDE Systems written by Jens Lang and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nowadays there is an increasing emphasis on all aspects of adaptively gener ating a grid that evolves with the solution of a PDE. Another challenge is to develop efficient higher-order one-step integration methods which can handle very stiff equations and which allow us to accommodate a spatial grid in each time step without any specific difficulties. In this monograph a combination of both error-controlled grid refinement and one-step methods of Rosenbrock-type is presented. It is my intention to impart the beauty and complexity found in the theoretical investigation of the adaptive algorithm proposed here, in its realization and in solving non-trivial complex problems. I hope that this method will find many more interesting applications. Berlin-Dahlem, May 2000 Jens Lang Acknowledgements I have looked forward to writing this section since it is a pleasure for me to thank all friends who made this work possible and provided valuable input. I would like to express my gratitude to Peter Deuflhard for giving me the oppor tunity to work in the field of Scientific Computing. I have benefited immensly from his help to get the right perspectives, and from his continuous encourage ment and support over several years. He certainly will forgive me the use of Rosenbrock methods rather than extrapolation methods to integrate in time.
Download or read book Space Time Methods written by Ulrich Langer and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-09-23 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides an introduction to modern space-time discretization methods such as finite and boundary elements and isogeometric analysis for time-dependent initial-boundary value problems of parabolic and hyperbolic type. Particular focus is given on stable formulations, error estimates, adaptivity in space and time, efficient solution algorithms, parallelization of the solution pipeline, and applications in science and engineering.
Download or read book Multilevel Adaptive Methods for Partial Differential Equations written by Stephen F. McCormick and published by SIAM. This book was released on 1989-01-01 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: A practical handbook for understanding and using fast adaptive composite grid (FAC) methods for discretization and solution of partial differential equations (PDEs). Contains fundamental concepts. These so-called FAC are characterized by their use of a composite grid, which is nominally the union of various uniform grids. FAC is capable of producing a composite grid with tailored resolution, and a corresponding solution with commensurate accuracy, at a cost proportional to the number of composite grid points. Moreover, special asynchronous versions of the fast adaptive composite grid methods (AFAC) studied here have seemingly optimal complexity in a parallel computing environment. Most of the methods treated in this book were discovered only within the last decade, and in many cases their development is still in its infancy. While this is not meant to be comprehensive, it does provide a theoretical and practical guide to multilevel adaptive methods and relevant discretization techniques.
Download or read book The Gradient Discretisation Method written by Jérôme Droniou and published by Springer. This book was released on 2018-07-31 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents the Gradient Discretisation Method (GDM), which is a unified convergence analysis framework for numerical methods for elliptic and parabolic partial differential equations. The results obtained by the GDM cover both stationary and transient models; error estimates are provided for linear (and some non-linear) equations, and convergence is established for a wide range of fully non-linear models (e.g. Leray–Lions equations and degenerate parabolic equations such as the Stefan or Richards models). The GDM applies to a diverse range of methods, both classical (conforming, non-conforming, mixed finite elements, discontinuous Galerkin) and modern (mimetic finite differences, hybrid and mixed finite volume, MPFA-O finite volume), some of which can be built on very general meshes.span style="" ms="" mincho";mso-bidi-font-family:="" the="" core="" properties="" and="" analytical="" tools="" required="" to="" work="" within="" gdm="" are="" stressed,="" it="" is="" shown="" that="" scheme="" convergence="" can="" often="" be="" established="" by="" verifying="" a="" small="" number="" of="" properties.="" scope="" some="" featured="" techniques="" results,="" such="" as="" time-space="" compactness="" theorems="" (discrete="" aubin–simon,="" discontinuous="" ascoli–arzela),="" goes="" beyond="" gdm,="" making="" them="" potentially="" applicable="" numerical="" schemes="" not="" (yet)="" known="" fit="" into="" this="" framework.span style="font-family:" ms="" mincho";mso-bidi-font-family:="" this="" monograph="" is="" intended="" for="" graduate="" students,="" researchers="" and="" experts="" in="" the="" field="" of="" numerical="" analysis="" partial="" differential="" equations./ppiiiiibr/i/i/i/i/i/p
Download or read book Exposition des sculptures de Degas written by and published by . This book was released on 1921 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An adaptive multilevel approach to parabolic equations written by Folkmar A. Bornemann and published by . This book was released on 1990 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Adaptive Numerical Solution of PDEs written by Peter Deuflhard and published by Walter de Gruyter. This book was released on 2012-08-31 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the general topic “Numerical solution of partial differential equations (PDEs)” with a focus on adaptivity of discretizations in space and time. By and large, introductory textbooks like “Numerical Analysis in Modern Scientific Computing” by Deuflhard and Hohmann should suffice as a prerequisite. The emphasis lies on elliptic and parabolic systems. Hyperbolic conservation laws are treated only on an elementary level excluding turbulence. Numerical Analysis is clearly understood as part of Scientific Computing. The focus is on the efficiency of algorithms, i.e. speed, reliability, and robustness, which directly leads to the concept of adaptivity in algorithms. The theoretical derivation and analysis is kept as elementary as possible. Nevertheless required somewhat more sophisticated mathematical theory is summarized in comprehensive form in an appendix. Complex relations are explained by numerous figures and illustrating examples. Non-trivial problems from regenerative energy, nanotechnology, surgery, and physiology are inserted. The text will appeal to graduate students and researchers on the job in mathematics, science, and technology. Conceptually, it has been written as a textbook including exercises and a software list, but at the same time it should be well-suited for self-study.
Download or read book Moving grid Methods for Time dependent Partial Differential Equations written by P. A. Zegeling and published by . This book was released on 1993 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Adaptive Multilevel Approach to Parabolic Equations III written by Folkmar A. Bornemann and published by . This book was released on 1991 with total page 47 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "Part III of the paper is devoted to the construction of an adaptive FEM solver in two spatial dimensions, which is able to handle the singularly perturbed elliptic problems arising from discretization in time. The problems of error estimation and multilevel iterative solution of the linear systems -- both uniformly well behaved with respect to the time step -- can be solved simultaneously within the framework of preconditioning. A multilevel nodal basis preconditioner able to handle highly nonuniform meshes is derived. As a numerical example an application of the method to the bioheat-transfer equation is included."
Download or read book Self Adaptive Methods for Parabolic Partial Differential Equations written by Dennis B. Gannon and published by . This book was released on 1980 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book PETSc for Partial Differential Equations Numerical Solutions in C and Python written by Ed Bueler and published by SIAM. This book was released on 2020-10-22 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Portable, Extensible Toolkit for Scientific Computation (PETSc) is an open-source library of advanced data structures and methods for solving linear and nonlinear equations and for managing discretizations. This book uses these modern numerical tools to demonstrate how to solve nonlinear partial differential equations (PDEs) in parallel. It starts from key mathematical concepts, such as Krylov space methods, preconditioning, multigrid, and Newton’s method. In PETSc these components are composed at run time into fast solvers. Discretizations are introduced from the beginning, with an emphasis on finite difference and finite element methodologies. The example C programs of the first 12 chapters, listed on the inside front cover, solve (mostly) elliptic and parabolic PDE problems. Discretization leads to large, sparse, and generally nonlinear systems of algebraic equations. For such problems, mathematical solver concepts are explained and illustrated through the examples, with sufficient context to speed further development. PETSc for Partial Differential Equations addresses both discretizations and fast solvers for PDEs, emphasizing practice more than theory. Well-structured examples lead to run-time choices that result in high solver performance and parallel scalability. The last two chapters build on the reader’s understanding of fast solver concepts when applying the Firedrake Python finite element solver library. This textbook, the first to cover PETSc programming for nonlinear PDEs, provides an on-ramp for graduate students and researchers to a major area of high-performance computing for science and engineering. It is suitable as a supplement for courses in scientific computing or numerical methods for differential equations.
Download or read book An Adaptive Multilevel Approach to Parabolic Equations in Two Space Dimensions written by Folkmar Bornemann and published by . This book was released on 1991 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Advanced Finite Element Methods with Applications written by Thomas Apel and published by Springer. This book was released on 2019-06-28 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite element methods are the most popular methods for solving partial differential equations numerically, and despite having a history of more than 50 years, there is still active research on their analysis, application and extension. This book features overview papers and original research articles from participants of the 30th Chemnitz Finite Element Symposium, which itself has a 40-year history. Covering topics including numerical methods for equations with fractional partial derivatives; isogeometric analysis and other novel discretization methods, like space-time finite elements and boundary elements; analysis of a posteriori error estimates and adaptive methods; enhancement of efficient solvers of the resulting systems of equations, discretization methods for partial differential equations on surfaces; and methods adapted to applications in solid and fluid mechanics, it offers readers insights into the latest results.
Download or read book Adaptive Space meshing Strategies for the Numerical Solution of Parabolic Partial Differential Equations in One Space Dimension written by Paul P. Neary and published by . This book was released on 1990 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An adaptive multilevel approach ro parabolic equations in two space dimensions written by Folkmar A. Bornemann and published by . This book was released on 1991 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt:
