Analysis of HDG method for the reaction-diffusion equations

Sayari, Sayed; Zaghdani, Abdelhamid; Hajji, Miled El

doi:10.1016/j.apnum.2020.05.012

Cited by 3 publications

(2 citation statements)

References 20 publications

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“…By using the rule Therefore, the largest invariant set contained in the set {(S, E, I, R) | Ḟ2 = 0} is reduced to the singleton set {E * }. Applying LaSalle's invariance principle [14] (see [18,19,20,21,22,23] for other applications), one can deduce that E * is GAS when R > 1.…”

Section: Global Stability Analysismentioning

confidence: 99%

Mathematical Analysis of a SEIR Model with Nonlinear Incidence Rate for COVID-19 Dynamics

Alhmadi¹

2022

ARJOM

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In this paper, an SEIR epidemic model with nonlinear incidence is considered. First, we formulate the model and obtain its basic properties. Then, we find the equilibrium points of the model, the disease-free and the endemic equilibrium. The stability of disease-free and endemic equilibrium is associated with the basic reproduction number R. If the basic reproduction number \(\mathcal{R}\) < 1, the disease-free equilibrium \(\mathcal{E}\) is locally as well as globally asymptotically stable. Moreover, if the basic reproduction number \(\mathcal{R}\) > 1, the disease is uniformly persistent and the unique endemic equilibrium \(\mathcal{E}\) * of the system is locally as well as globally asymptotically stable under certain conditions. Finally, the numerical results justify the analytical results.

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Section: Global Stability Analysismentioning

confidence: 99%

Mathematical Analysis of a SEIR Model with Nonlinear Incidence Rate for COVID-19 Dynamics

Alhmadi¹

2022

ARJOM

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“…Recently, Lin Mu and his collaborators [9] construct a new WG-FEM which discretizes the second order elliptic equation in non-mixed form directly, and admit general finite element partitions consisting of arbitrary polytopal elements. The Weak Galerkin mixed finite element method is an extension of weak Galerkin finite element method [14] and it was used for the numerical resolution of partial differential equations [4,6,10,15], In [14], a mixed WG-FEM has been introduced and analysed for the second order elliptic equation, in which the utilization of stabilization for the flux variable has an important role in the mixed formulation. In this paper, we are interested with the development of weak Galerkin mixed formulation for the Maxwell problem which consists in finding two unknown functions u and p such that…”

Section: Introductionmentioning

confidence: 99%

Analysis of aWeak Galerkin Mixed Formulation for Maxwell’s Equations

ZAGHDANI,

HASNAOUI1,

SAYARI

2024

KgJMat

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In this paper we introduce and analyse a mixed weak Galekin ﬁnite element method for the Maxwell equations in the primary electric ﬁeld-Lagrange multiplier. Our weak Galerkin method is equipped with stable ﬁnite elements composed of habitual polynomials of degree k for the electric ﬁeld and polynomials of degree k + 1 for the Lagrange multiplier. Optimal order error estimations for the proposed weak Galerkin mixed ﬁnite element formulation are demonstrated and are conﬁrmed numerically on a two dimensional bounded domain.

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Analysis of a Weak Galerkin Mixed Formulation for Modified Maxwell’s Equations

Zaghdani,

Hasnaoui

2024

Mathematics

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In this paper, we are interested in studying a mixed formulation of weak Galerkin type to approach the electric field and a Lagrange multiplier, which are solutions of a problem deriving from Maxwell’s equations. Our numerical scheme is formed with stable finite elements constructed of usual polynomials of degree k for the electric field and of degree k+1 for the Lagrange multiplier; its consistency and well-posedness are shown. Some optimal error estimates are proven and tested numerically in a bounded subdomain of R2.

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Analysis of HDG method for the reaction-diffusion equations

Cited by 3 publications

References 20 publications

Mathematical Analysis of a SEIR Model with Nonlinear Incidence Rate for COVID-19 Dynamics

Mathematical Analysis of a SEIR Model with Nonlinear Incidence Rate for COVID-19 Dynamics

Analysis of aWeak Galerkin Mixed Formulation for Maxwell’s Equations

Analysis of a Weak Galerkin Mixed Formulation for Modified Maxwell’s Equations

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