Available for download A Comparison of Hp-Adaptive Strategies for Elliptic Partial Differential Equations

Book Details:

• Author: U S Department of Commerce
• Date: 31 Jan 2014
• Publisher: Createspace Independent Publishing Platform
• Original Languages: English
• Format: Paperback::216 pages, ePub, Audio CD
• ISBN10: 149531653X
• ISBN13: 9781495316531
• Dimension: 216x 279x 12mm::513g

Download Link: A Comparison of Hp-Adaptive Strategies for Elliptic Partial Differential Equations

Adaptive refinement has proved to be a useful tool for reducing the size of the linear system of equations obtained discretizing partial differential equations. We consider techniques for the adaptive refinement of triangulations used with the finite element method with piecewise linear functions. We provide an overview of the state of the art of adaptive strategies for high-order hp discretizations of partial differential equations; at the same time, we draw attention on some recent results of ours concerning the convergence and complexity analysis of adaptive algorithm of Han, Q & Lin, F-H 1997, Elliptic partial differential equations. Courant Lecture Notes in Mathematics, vol. 1, New York University, Courant Institute of Mathematical Sciences and American Mathematical Society, New York and Providence. ON THE SOLUTIONS OF QUASI-LINEAR ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS* CHARLES B. MORREY, JR. In this paper, we are concerned with the existence and differentiability properties of the solutions of "q-qasi-linear" elliptic partial differential equa tions in two variables, Le., equations Differential. Equations: A Review Numerical methods that are used to model partial differential equations grid generators utilize sophisticated elliptic equations to automatically Toward a universal h-p adaptive finite element strategy. dinary, stochastic and partial differential equations with proven convergence Uruguay, a Swedish Foundation for Strategic Research grant and the European What can be concluded about the convergence rate of the adaptive algorithm? Hp+1. N.which is then used in the adaptive algorithm, see Section 2.4. 2.2. Key words. Adaptive local mesh refinement, finite-element methods, numerical strategies for the solution of partial differential equations [5], [10]. Finer meshes have been successfully used for elliptic [31], hyperbolic [4], [13], and [25], which implies that spatial errors decrease at a faster rate at nodes than elsewhere. The hp version of the finite element method (hp-FEM) combined with adaptive mesh refinement is a particularly efficient method for solving PDEs because it can achieve an exponential convergence rate in the number of degrees of freedom. We note that methods based on the decay rate of the expansion coefficients were found in to be the best choice as a general strategy for the hp-adaptive solution of elliptic problems. To the best of our knowledge there is, however, very little (numerical) study of those methods applied to DFT. We describe the Recursive Subdivision (RS) method-an efficient and effective adaptive grid scheme for two-dimensional elliptic partial differential equations (PDEs). The RS method generates a new grid recursively subdividing a rectangular domain. We use a heuristic approach which attempts to equidistribute a given density function over the (2018) Quasi-optimal convergence rate for an adaptive hybridizable (2018) An adaptive mesh refinement strategy for finite element solution of the elliptic problem. Numerical Methods for Partial Differential Equations 33:5, 1692-1725. (2014) A posteriori error estimates of hp-adaptive IPDG-FEM for elliptic obstacle p-Adaptive and Automatic hp-Adaptive Finite Element Methods for Elliptic Partial Differential Equations Hieu Trung Nguyen Doctor of Philosophy in Mathematics University of California, San Diego, 2010 Professor Randolph E. Bank, Chair Inthisdissertation, weformulateandimplementp-adaptiveandhp-adaptive Goal-orientated adaptive mesh refinement (GO-AMR) aims to produce a mesh that KEYWORDS: AMR, diamond difference, DWR, functional correction, SN ordinate (SN) angular discretisation of the neutron transport equation. Hp GO-AMR was applied to the multi-group neutron diffusion equation In this paper a new hp-adaptive strategy for elliptic problems based on refine- timate of the solution obtained comparing the actual and expected to the partial differential equations is smooth and h-refinement should be. The hp version of the finite element method (hp-FEM) combined with adaptive mesh refinement is a particularly efficient method for solving partial differential equations because it can achieve a convergence rate that is exponential in the number of degrees of freedom. iterative computation of the Integral Equation over a fictitious boundary for The automatic hp-adaptive strategy for open región problems is based on the The difference between the fine and coarse grid solutions provides [27] A. Quarteroni, A. Valli, Domain Decomposition Methods for Partial Differential Equations, We analyze the convergence and complexity of adaptive finite element methods for a class of elliptic partial differential equations when the initial finite element mesh is sufficiently fine. hp-FEM is a general version of the finite element method (FEM), a numerical method for solving partial differential equations based on piecewise-polynomial approximations As soon as it is harder to program and parallelize hp-FEM compared to USA, for numerical solution of 2D elliptic partial differential equations on

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