| 1. |
- Asadzadeh, Mohammad, 1952, et al.
(författare)
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On Convergence of the Streamline Diffusion and Discontinuous Galerkin Methods for the Multi-Dimensional Fermi Pencil Beam Equation
- 2013
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Ingår i: International Journal of Numerical Analysis and Modeling. - 1705-5105. ; 10:4, s. 860-875
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Tidskriftsartikel (refereegranskat)abstract
- We derive error estimates in the L-2 norms, for the streamline diffusion (SD) and discontinuous Galerkin (DG) finite element methods for steady state, energy dependent, Fermi equation in three space dimensions. These estimates yield optimal convergence rates due to the maximal available regularity of the exact solution. Here our focus is on theoretical aspects of the h and hp approximations in both SD and DG settings.
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| 2. |
- Bozorgnia, Farid, et al.
(författare)
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Numerical Schemes for Multi Phase Quadrature Domains
- 2014
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Ingår i: International Journal of Numerical Analysis & Modeling. - 1705-5105. ; 11:4, s. 726-744
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Tidskriftsartikel (refereegranskat)abstract
- In this work, numerical schemes to approximate the solution of one and multi phase quadrature domains are presented. We shall construct a monotone, stable and consistent finite difference method for both one and two phase cases, which converges to the viscosity solution of the partial differential equation arising from the corresponding quadrature domain theory. Moreover, we will discuss the numerical implementation of the resulting approach and present computational tests.
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| 3. |
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| 4. |
- Feng, Tao, et al.
(författare)
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Adaptive finite element methods for parameter estimation problems in linear elasticity
- 2009
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Ingår i: International Journal of Numerical Analysis & Modeling. - 1705-5105. ; 6:1, s. 17-32
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, the Lame coefficients in the linear elasticity problem are estimated by using the measurements of displacement. Some a posteriori error estimators for the approximation error of the parameters are derived, and then adaptive finite element schemes are developed for the discretization of the parameter estimation problem, based on the error estimators. The Gauss-Newton method is employed to solve the discretized nonlinear least-squares problem. Some numerical results are presented.
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| 5. |
- Muntean, Adrian, 1974-
(författare)
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Error bounds on semi-discrete finite element approximations of a moving-boundary system arising in concrete corrosion
- 2008
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Ingår i: International Journal of Numerical Analysis & Modeling. - 1705-5105. ; 5:3, s. 353-372
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Tidskriftsartikel (refereegranskat)abstract
- Finite element approximations of positive weak solutions to a onephase unidimensional moving-boundary system with kinetic condition describing the penetration of a sharp-reaction interface in concrete are considered. A priori and a posteriori error estimates for the semi-discrete fields of active concentrations and for the position of the moving interface are obtained. The important feature of the system of partial differential equations is that the nonlinear coupling occurs due to the presence of both the moving boundary and the non-linearities of localized sinks and sources by reaction.
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| 6. |
- Nepal, Surendra, et al.
(författare)
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Error estimates for semi-discrete finite element approximations for a moving boundary problem capturing the penetration of diffusants into rubber
- 2022
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Ingår i: International Journal of Numerical Analysis & Modeling. - : ISCI-INST SCIENTIFIC COMPUTING & INFORMATION. - 1705-5105. ; 19:1, s. 101-125
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Tidskriftsartikel (refereegranskat)abstract
- We consider a moving boundary problem with kinetic condition that describes the diffusion of solvent into rubber and study semi-discrete finite element approximations of the corresponding weak solutions. We report on both a priori and a posteriori error estimates for the mass concentration of the diffusants, and respectively, for the a priori unknown position of the moving boundary. Our working techniques include integral and energy-based estimates for a nonlinear parabolic problem posed in a transformed fixed domain combined with a suitable use of the interpolation-trace inequality to handle the interface terms. Numerical illustrations of our FEM approximations are within the experimental range and show good agreement with our theoretical investigation. This work is a preliminary investigation necessary before extending the current moving boundary modeling to account explicitly for the mechanics of hyperelastic rods to capture a directional swelling of the underlying elastomer.
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| 7. |
- Sorgentone, Chiara, et al.
(författare)
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A systematic method to construct mimetic Finite-Difference schemes for incompressible flows
- 2017
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Ingår i: International Journal of Numerical Analysis & Modeling. - : University of Alberta. - 1705-5105. ; 14:3, s. 419-436
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Tidskriftsartikel (refereegranskat)abstract
- We present a general procedure to construct a non-linear mimetic finite-difference operator. The method is very simple and general: it can be applied for any order scheme, for any number of grid points and for any operator constraints. In order to validate the procedure, we apply it to a specific example, the Jacobian operator for the vorticity equation. In particular we consider a finite difference approximation of a second order Jacobian which uses a 9x9 uniform stencil, verifies the skew-symmetric property and satisfies physical constraints such as conservation of energy and enstrophy. This particular choice has been made in order to compare the present scheme with Arakawa’s renowned Jacobian, which turns out to be a specific case of the general solution. Other possible generalizations of Arakawa’s Jacobian are available in literature but only the present approach ensures that the class of solutions found is the widest possible. A simplified analysis of the general scheme is proposed in terms of truncation error and study of the linearised operator together with some numerical experiments. We also propose a class of analytical solutions for the vorticity equation to compare an exact solution with our numerical results.
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