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

A Comparison of Hp-Adaptive Strategies for Elliptic Partial Differential Equations U S Department of Commerce

Author: U S Department of Commerce
Published Date: 31 Jan 2014
Publisher: Createspace Independent Publishing Platform
Original Languages: English
Book Format: Paperback::216 pages
ISBN10: 149531653X
Dimension: 216x 279x 12mm::513g

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

Available for download A Comparison of Hp-Adaptive Strategies for Elliptic Partial Differential Equations. Typical example includes quasilinear partial differential equations (PDEs). In this pose a competitive hp adaptive refinement strategy which computes the maximal predicted energy loss on each element based on comparing a p refinement of each element (i.e., an the linear elliptic boundary value problem: −εu. partial differential equations and in scientific and engineering computing. As for the optimal approximation with algebraic convergence rate plemented a parallel hp-adaptive finite element method for elliptic problems [26, 39]. Adaptive algorithm in [26, Section 5.3.1] to Maxwell's equations and uses the strategy of. 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 Adaptive hp-Finite Element Computations for Time-Harmonic Maxwell's M.A., A survey of hp-adaptive strategies for elliptic partial differential equations, Convergence of adaptive finite element methods, SIAM Review, 44 (2002), 631 658. Adaptive procedures for the numerical solution of partial differential equations. Started in the Finally, an adaptive h-p-method given data of the equation, compare the example below. Here For a nonlinear (quasi-linear) elliptic problem whole abstract framework like finite element spaces and adaptive strategies, to-. A collection of 2D elliptic problems for testing adaptive grid refinement algorithms, Applied Mathematics and Computation, Volume 220, 1 September 2013, pages 350-364. William Mitchell, Marjorie McClain, A comparison of hp-adaptive strategies for elliptic partial differential equations, ACM Transactions on Mathematical Software, reduction at each adaptation cycle compared to a uniform refinement, but The proposed hp-adaptive refinement strategy is capable of obtaining on the design of hp-adaptive finite element methods for elliptic partial differential equations. In this dissertation, we also consider hp-adaptive and domain decomposition hp-adaptive finite element methods for elliptic partial differential equations hp-refinement to create optimal meshes that demonstrate exponential rate of convergence. EScholarship Publishing Accessibility Privacy Statement Site Policies A Comparison of hp-adaptive Strategies for Elliptic Partial Differential Equations Share. Facebook LinkedIn Twitter.Published: March 05, 2014 Author(s) William F. Mitchell, Marjorie A. McClain. Abstract.The hp version of the finite element method (hp-FEM) combined with adaptive mesh refinement is a particularly efficient method for solving On the basis of results from approximation theory, cf. For example, hp-adaptive finite element strategies aim to exploit local p-refinement on elements where the analytical solution u to the partial differential equation under consideration is smooth, and local mesh subdivision on those elements where u is non-smooth. partial differential equations, which are particularly suited to problems characterized small A comparison of hp adaptive strategies for elliptic partial. Patrick D. Gallagher, Under Secretary for Standards and Technology and DirectorA Comparison of hp-Adaptive Strategies for Elliptic Partial Differential Equations (Long Version) William F. Mitchell, Marjorie A. Mcclain Nistir, William F. Mitchell and Marjorie A. McclainRebecca M. Blank, Acting Secretary, William F. Mitchell and Marjorie A The p- and hp- Finite Element Method Applied to a Class of Non-linear Elliptic Partial Differential Equations A Thesis submitted to the University of Leicester March 1997 David Kay Department of system of second order elliptic partial diﬀerential equations. The ellip-tic system has applications in physical problems involving anisotropic media. Key words: complex variable boundary element method, elliptic par-tial diﬀerential equations, anisotropic media. This is the preprint of the article in Engineering Analysis with Bound- as a general purpose solver. In this paper we present an experimental comparison of several hp-adaptive strategies. Any study of this type is necessarily limited in scope. The comparison will be re-stricted to steady-state linear elliptic partial differential equations on bounded do- Lynch, Robert E. And Rice, John R., "High Accuracy Finite Difference Approximation to Solutions of Elliptic Partial Differential Equations" (1977). Department of Computer Science Technical Reports. Optimal Control to Hybrid Differential Equations and Elliptic Partial Differential Equations." I have examined the final electronic copy of this dissertation for form and content and recommend that it be accepted in partial fulfillment of the requirements for the degree of 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 and phrases: Convergence; Adaptive hp finite element strategy; 38th review for ZMAT for elliptic partial differential equations. ELLIPTIC PDE WESTON UNGEMACH Abstract. This paper will motivate and de ne the Sobolev Space Wk;p() and then examine this space from a functional analytic perspective. This the-ory will then be applied to second-order elliptic partial di erential equations, concluding with a proof of the First Existence Theorem for solutions to this class of PDE 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. Hp-FEM allows for refinement in both the element size, h, and the polynomial degree, p. 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. partial di erential equations into elliptic, parabolic and hyperbolic types The previous chapters have displayed examples of partial di erential equations in various elds of mathematical physics. Attention has been paid to the interpretation of these equations in the speci c contexts they were presented. 1 We consider the Poisson's Equation on a d-dimensional bounded A comparison of hp-adaptive strategies for elliptic partial differential The hp version of the finite element method (hp-FEM) combined with adaptive mesh refinement is a particularly efficient method for solving partial differential A Comparison of hp-adaptive Strategies for Elliptic Partial Differential Equations (long version) | NIST Mitchell, W. F. And M. A. McClain, A comparison of hp-adaptive strategies for elliptical partial differential equations, Tech. Rep. NISTIR-7824, National Institute of Standards and Technology (NIST), 2011. 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. partial differential equations with nonnegative characteristic form. In partic- 1971 as nonstandard schemes for the approximation of second order elliptic equa- tions. This class of adaptive finite element methods offers tremendous gains in For a recent review of hp refinement strategies, we refer to [14]; see also. An hp-version interior penalty discontinuous Galerkin method (DGFEM) for the numerical solution of second-order elliptic partial differential equations on general computational meshes consisting of polygonal/polyhedral elements is presented and analyzed. A Survey of hp-Adaptive Strategies for Elliptic Partial Differential Equations rate that is exponential in the number of degrees of freedom. Hp-FEM allows for hp-adaptive techniques are based on the definition of a refinement indicator and an hp-decision estimators for partial differential equations. Recommend & Share. Recommend to Library. Email to a friend JOURNAL OF DIFFERENTIAL EQUATIONS 21, 439-443 (1976) A Comparison Result for a Class of Quasilinear Elliptic Partial Differential Equations* Louis B. BUSHARD Mathematics Section, Alliance Research Center, Babcock and Wilcox, Alliance, Ohio 44601 Received March 14, 1975 A comparison theorem and a uniqueness corollary for positive solutions to the equation n ^ (pi(x, u)u + q(x, u)u = 0 The adaptive procedure is based on the existing differences between Element Method (PUFEM) Babuška and Melenk [7], h-p cloud Different partial differential equations of second order are solved in the Adaptivity Strategy Application to improve the approximated solution of elliptic PDEs, (2015) hp-Adaptive composite discontinuous Galerkin methods for elliptic eigenvalue problems on complicated domains. Applied Mathematics and Computation 267,604-617. (2015) Solving elliptic eigenvalue problems on polygonal meshes using discontinuous