A mixed-hybrid finite element method for convection–diffusion problems

Farhloul, Mohamed; Mounim, A. Serghini

doi:10.1016/j.amc.2005.01.101

Cited by 12 publications

(9 citation statements)

References 5 publications

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“…Since the estimate (19) uses an inverse inequality, the constant c I depends on the shapes of the elements. Lemma 1 now allows us to construct a suitable test function for establishing the following stability estimate.…”

Section: Pure Diffusion -Methodsmentioning

confidence: 99%

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A hybrid mixed discontinuous Galerkin finite-element method for convection-diffusion problems

Egger

Schöberl

2009

IMA Journal of Numerical Analysis

131

120

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We propose and analyse a new finite element method for convection diffusion problems based on the combination of a mixed method for the elliptic and a discontinuous Galerkin method for the hyperbolic part of the problem. The two methods are made compatible via hybridization and the combination of both is appropriate for the solution of intermediate convection-diffusion problems. By construction, the discrete solutions obtained for the limiting subproblems coincide with the ones obtained by the mixed method for the elliptic and the discontinuous Galerkin method for the limiting hyperbolic problem, respectively. We present a new type of analysis that explicitly takes into account the Lagrange-multipliers introduced by hybridization. The use of adequate energy norms allows to treat the purely diffusive, the convection dominated, and the hyperbolic regime in a unified manner. In numerical tests, we illustrated the efficiency of our approach and compare to results obtained with other methods for convection diffusion problems.

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Section: Pure Diffusion -Methodsmentioning

confidence: 99%

“…For diffusion dominated regions, the stabilization can be omitted yielding a scheme that was studied numerically in 1D in [19]. Our analysis in Section 4.2 also includes this case.…”

Section: Introductionmentioning

confidence: 99%

A hybrid mixed discontinuous Galerkin finite-element method for convection-diffusion problems

Egger

Schöberl

2009

IMA Journal of Numerical Analysis

131

120

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“…Therefore, the method is extended to hybrid form where a Lagrange multiplier is added to MFE system. The new mixed hybrid finite element (MHFE) system enforce interelement mass continuity not by the means of flux but by the Lagrange multiplier, which is projected variable p of element center onto the element faces (Farhloul and Mounim, 2005). MHFE method results in a symmetric positivedefinite system which is easier to solve.…”

Section: Contributors Equation Literaturesmentioning

confidence: 99%

CO₂ flow in saline aquifer with salt precipitation

Pau

Pao

Yong

2016

International Journal of Numerical Methods for Heat &Amp; Fluid Flow

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Purpose -The purpose of this paper is to introduce the solution to two-phase flow in CO 2 /brine system with salt precipitation by applying mixed hybrid finite element (MHFE) method to pressure equation and finite volume (FV) method to saturation equation. Mixed finite element method solves pressure and velocity in two subspaces while hybrid method is an extension of mixed method, where the Lagrange multiplier is added to the former in order to ensure the continuity from one element to the adjacent elements. The authors propose the modeling of salt precipitation using core flood experimental result and adapt to be applicable for numerical modeling. Design/methodology/approach -The governing equations are discretized using Mixed Hybrid Finite Element-Finite Volume (MHFE-FV) method. This method has the feature of localized conservation which is attractive for application on heterogeneous porous media. In addition to this, the salt precipitation effect is modeled using the data from core flood experiment (Ott et al., 2011). The random data are linearized to obtain the relationship between salt precipitate and CO 2 saturation and implemented to the algorithm for two-phase flow in CO 2 and brine system. Findings -The solution of MHFE-FV scheme has good agreement with the solution using implicit pressure and explicit saturation (IMPES) reported by Negara et al. (2011), with average error of 4.20 percent. Localized conservation is demonstrated in the case of randomized heterogeneous porous media where fingering effects are explicitly observed. Salt precipitation prediction using the proposed method is able to predict the decrement of porosity by 16.71 percent and permeability by 22.19 percent. This results in the decreased amount of CO 2 injected by 64.70 percent.Research limitations/implications -This paper presents the solution of two-phase flow in CO 2 brine system during CO 2 injection in saline aquifer using MHFE-FV method with the additional salt precipitation model obtained based on core flood experiment result. Practical implications -A methodology to predict the salt precipitation based on CO 2 saturation. Social implications -Contribution to green house gas reduction. Originality/value -The authors use MHFE-FV to solve hyperbolic PDE to obtain accurate results of CO 2 saturation, and subsequently use this to compute the salt precipitation.

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“…To remedy the source of numerical instability, upwind methods are employed. Various upwind techniques have been proposed and are employed in finite difference solutions (see for example [1] and references therein), finite volume and mixed finite element solutions (see for example [2][3][4][5] and references therein), and smoothed particle hydrodynamics (SPH) method (see for example [6] and references therein). However, this effort has been mainly done in the field of finite differences, finite elements, and finite volumes.…”

Section: F Colin R Egli and A Serghini Mounimmentioning

confidence: 99%

A stabilized meshfree reproducing kernel‐based method for convection–diffusion problems

Colin

Egli

Mounim

2011

Numerical Meth Engineering

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SUMMARYIn this paper, we develop a meshfree particle-based method for convection-diffusion problems. Discretization is performed by using piecewise constant kernels. The stabilized scheme is based on a new upwind kernel. We show that accurate and stable scheme can be obtained by using purpose-built kernels. It also shown that under some conditions the classical optimal finite difference scheme can be derived by the new method. Several numerical tests validate the method.

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A mixed-hybrid finite element method for convection–diffusion problems

Cited by 12 publications

References 5 publications

A hybrid mixed discontinuous Galerkin finite-element method for convection-diffusion problems

A hybrid mixed discontinuous Galerkin finite-element method for convection-diffusion problems

CO₂ flow in saline aquifer with salt precipitation

A stabilized meshfree reproducing kernel‐based method for convection–diffusion problems

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A mixed-hybrid finite element method for convection–diffusion problems

Cited by 12 publications

References 5 publications

A hybrid mixed discontinuous Galerkin finite-element method for convection-diffusion problems

A hybrid mixed discontinuous Galerkin finite-element method for convection-diffusion problems

CO2 flow in saline aquifer with salt precipitation

A stabilized meshfree reproducing kernel‐based method for convection–diffusion problems

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CO₂ flow in saline aquifer with salt precipitation