A Local Refinement Finite Element Method For Time Dependent Partial Differential Equations
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A Local Refinement Finite Element Method For Time Dependent Partial Differential Equations
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Author : J. E. Flaherty
language : en
Publisher:
Release Date : 1984
A Local Refinement Finite Element Method For Time Dependent Partial Differential Equations written by J. E. Flaherty and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with categories.
The authors discuss an adaptive local refinement finite element method for solving initial-boundary value problems for vector systems of partial differential equations in one space dimension and time. The method ues piecewise bilinear rectangular space-time finite elements. For each time step, grids are automatically added to regions where the local discretization error is estimated as being larger than a prescribed tolerance. The authors discuss several aspects oof their algorithm, including the tree structure that is used to represent the finite element solution and grids, an error estimation technique, and initial boundary conditions at coarse-fine mesh interfaces. The authors also present computational results for a simple linear hyperbolic problem, a problem involving Burger's equation, and a model combustion problem. Originator-supplied keywords include: Adaptive methods, Finite element methods, Local refinement, and Time dependent problems.
An Adaptive Mesh Moving And Local Refinement Method For Time Dependent Partial Differential Equations
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Author :
language : en
Publisher:
Release Date : 1990
An Adaptive Mesh Moving And Local Refinement Method For Time Dependent Partial Differential Equations written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with categories.
We discuss mesh-moving, static mesh regeneration, and local mesh-refinement algorithms that can be used with a finite difference or finite element scheme to solve initial boundary value problems for vector systems of time-dependent partial differential equations in two space dimensions and time. A coarse based mesh of quadrilateral cells is moved by an algebraic mesh-movement function so as to follow and isolate spatially distinct phenomena. The local mesh-refinement method recursively divides the time step and spatial cells of the moving base mesh in regions where error indicators are high until a prescribed tolerance is satisfied. The static mesh-regeneration procedure is used to create a new base mesh when the existing one becomes to distorted. The adaptive methods have been combined with a MacCormack finite difference scheme for hyperbolic systems and an error indicator based upon estimates of the local discretization error obtained by Richardson extrapolation. Results are presented for several computational examples.
A Moving Finite Element Method For Time Dependent Partial Differential Equations With Error Estimation And Refinement
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Author : S. Adjerid
language : en
Publisher:
Release Date : 1984
A Moving Finite Element Method For Time Dependent Partial Differential Equations With Error Estimation And Refinement written by S. Adjerid and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with categories.
The authors discuss a moving finite element method for solving vector systems of time dependent partial differential equations in one space dimension. The mesh is moved so as to equidistribute the spatial component of the discretization error in H1. They present a method of estimating this error by using p-hierarchic finite elements. The error estimate is also used in an adaptive mesh refinement procedure to give an algorithm that combines mesh movement and refinement. The authors discretize the partial differential equations in space using a Galerkin procedure with piecewise linear elements to approximate the solution and quadratic elements to estimate the error. A system of ordinary differential equations for mesh velocities are used to control element motions. The authors use existing software for stiff ordinary differential equations for the temporal integration of the solution, the error estimate, and the mesh motion. Computational results using a code based on this method are presented for several examples.
An Adaptive Method With Mesh Moving And Local Mesh Refinement For Time Dependent Partial Differential Equations
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Author : David C. Arney
language : en
Publisher:
Release Date : 1988
An Adaptive Method With Mesh Moving And Local Mesh Refinement For Time Dependent Partial Differential Equations written by David C. Arney and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with categories.
The authors discuss mesh moving, static mesh regeneration, and local mesh refinement algorithms that can be used with a finite difference or finite element scheme to solve initial-boundary value problems for vector systems of time-dependent partial differential equations in two-space dimensions and time. A coarse base mesh of quadrilateral cells is moved by an algebraic mesh movement function so that it may follow and isolate spatially distinct phenomena. The local mesh refinement method recursively divides the time step and spatial cells of the moving base mesh in regions were error indicators are high until a prescribed tolerance is satisfied. The static mesh regeneration procedure is used to create a new base mesh when the existing ones become too distorted. In order to test our adaptive algorithms, the authors implemented them in a system code with an initial mesh generator, a MacCormack finite difference scheme for hyperbolic systems, and an error indicator based upon estimates of the local discretization error obtained by Richardson extrapolation. Results are presented for several computational examples. (kr).
A Moving Mesh Finite Element Method With Local Refinement For Parabolic Partial Differential Equations
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Author : Slimane Adjerid
language : en
Publisher:
Release Date : 1985
A Moving Mesh Finite Element Method With Local Refinement For Parabolic Partial Differential Equations written by Slimane Adjerid and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with categories.
An Adaptive Local Mesh Refinement Method For Time Dependent Partial Differential Equations
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Author : David C. Arney
language : en
Publisher:
Release Date : 1986
An Adaptive Local Mesh Refinement Method For Time Dependent Partial Differential Equations written by David C. Arney and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with categories.
Adaptive Refinement Methods For Nonlinear Parabolic Partial Differential Equations
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Author : M. Bietermman
language : en
Publisher:
Release Date : 1984
Adaptive Refinement Methods For Nonlinear Parabolic Partial Differential Equations written by M. Bietermman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with categories.
This document considers two adaptive finite element techniques for parabolic partial differential equations (PDEs) that are based on using error estimates to control mesh refinement. One technique is a method of lines approach that uses a Galerkin method to discretize the PDEs in space and implicit multi-step integration in time. Spatial elements are added and deleted in regions of high and low error and are all advanced with the same sequence of varying time steps. The second technique is a local refinement method that uses Galerkin approximations in both space and time. Fine grids of space-time elements are added to coarser grids and the problem is recursively solved in regions of high error. (Author).
Unstructured Space Time Finite Element Methods In Four Dimensions
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Author : David Charles Lenz
language : en
Publisher:
Release Date : 2020
Unstructured Space Time Finite Element Methods In Four Dimensions written by David Charles Lenz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with categories.
Large-scale simulations of time-dependent partial differential equations are, at present, largely reliant on massively parallel computers. As a result, the parallel scalability of numerical methods for partial differential equations is of crucial importance. In recent years, continuous space-time finite element methods have emerged as a promising technique for approximating these equations in a scalable, flexible way. In a space-time finite element method, the space and time variables of a time-dependent equation are treated as a single unified variable in higher-dimensional space. The higher-dimensional space-time domain is discretized into a collection of simplices and finite element methods may then be defined over this discretization. Parallelization is then achieved through domain decomposition techniques. In this dissertation, we extend the theory of space-time finite element methods to a more general class of problems. We prove new theoretical results describing the stability of space-time methods applied to parabolic partial differential equations with nontrivial convection and reaction terms. In particular, we define a streamline-upwind scheme which upwinds in the direction of the space-time convection. The stabilized method is proved to be coercive with respect to an energy norm and asymptotic error bounds are derived. This dissertation also proposes several operations for the construction and refinement of unstructured, conforming four-dimensional simplex meshes. We define a simple algorithm which takes as input any tetrahedral mesh and produces a corresponding four-dimensional, simplicial space-time mesh. Our algorithm always produces conforming triangulations and may be run concurrently for each spatial element. In addition, we describe how four-dimensional simplex elements can be bisected in order to achieve local spatiotemporal refinement.
An Adaptive Mesh Moving And Local Refinement Method For Time Dependent Partial Differential Equations
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Author : David C. Arney
language : en
Publisher:
Release Date : 1987
An Adaptive Mesh Moving And Local Refinement Method For Time Dependent Partial Differential Equations written by David C. Arney and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with categories.
A Review Of A Posteriori Error Estimation And Adaptive Mesh Refinement Techniques
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Author : Rüdiger Verführt
language : en
Publisher: Springer
Release Date : 1996-07
A Review Of A Posteriori Error Estimation And Adaptive Mesh Refinement Techniques written by Rüdiger Verführt and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-07 with Mathematics categories.