One-dimensional adaptive grid generation.

Khodier, Ahmed M.M.; Hassan, Adel Y.

Displaying similar documents to “One-dimensional adaptive grid generation.”

A comparison of the String Gradient Weighted Moving Finite Element method and a Parabolic Moving Mesh Partial Differential Equation method for solutions of partial differential equations

Abigail Wacher (2013)

Open Mathematics

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We compare numerical experiments from the String Gradient Weighted Moving Finite Element method and a Parabolic Moving Mesh Partial Differential Equation method, applied to three benchmark problems based on two different partial differential equations. Both methods are described in detail and we highlight some strengths and weaknesses of each method via the numerical comparisons. The two equations used in the benchmark problems are the viscous Burgers’ equation and the porous medium...

Minimization of functional majorant in a posteriori error analysis based on $H$ (div) multigrid-preconditioned CG method.

Valdman, Jan (2009)

Advances in Numerical Analysis

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ALBERT---Software for scientific computations and applications.

Schmidt, Alfred, Siebert, K.G. (2001)

Acta Mathematica Universitatis Comenianae. New Series

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A numerical method for a singularly perturbed three-point boundary value problem.

Çakır, Musa, Amiraliyev, Gabil M. (2010)

Journal of Applied Mathematics

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High-order compact implicit difference methods for parabolic equations in geodynamo simulation.

Liu, Don, Kuang, Weijia, Tangborn, Andrew (2009)

Advances in Mathematical Physics

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Hybrid parallelization of an adaptive finite element code

Axel Voigt, Thomas Witkowski (2010)

Kybernetika

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We present a hybrid OpenMP/MPI parallelization of the finite element method that is suitable to make use of modern high performance computers. These are usually built from a large bulk of multi-core systems connected by a fast network. Our parallelization method is based firstly on domain decomposition to divide the large problem into small chunks. Each of them is then solved on a multi-core system using parallel assembling, solution and error estimation. To make domain decomposition...

Anisotropic mesh adaption: application to computational fluid dynamics

Simona Perotto (2005)

Bollettino dell'Unione Matematica Italiana

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In this communication we focus on goal-oriented anisotropic adaption techniques. Starting point has been the derivation of suitable anisotropic interpolation error estimates for piecewise linear finite elements, on triangular grids in $2 D$ . Then we have merged these interpolation estimates with the dual-based a posteriori error analysis proposed by R. Rannacher and R. Becker. As examples of this general anisotropic a posteriori analysis, elliptic, advection-diffusion-reaction and the Stokes...

An adaptive finite element method for Fredholm integral equations of the first kind and its verification on experimental data

Nikolay Koshev, Larisa Beilina (2013)

Open Mathematics

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We propose an adaptive finite element method for the solution of a linear Fredholm integral equation of the first kind. We derive a posteriori error estimates in the functional to be minimized and in the regularized solution to this functional, and formulate corresponding adaptive algorithms. To do this we specify nonlinear results obtained earlier for the case of a linear bounded operator. Numerical experiments justify the efficiency of our a posteriori estimates applied both to the...