2026Journal article
Characteristic method for a coupled model of the fluid flow with nonlinear slip boundary conditions
Dania Ati, Rahma Agroum, M. Mbehou, Toni Sayah
CALCOLO
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Chargé de Cours
Scientific activity
Researcher profile
Faculty researcher at the University of Yaoundé I. Grade: Chargé de Cours.
Scientific publications
Dania Ati, Rahma Agroum, M. Mbehou, Toni Sayah
CALCOLO
P. Njeutcha Methouchelah, G. Chendjou, M.S. Daoussa Haggar, M. Mbehou
Results in Applied Mathematics
Mahamat Saleh Daoussa Haggar, K. Mahamat Malloum, Jean-Marcel Fokam, M. Mbehou
Computers & Mathematics with Applications
Raouda Amine Oumar, M. Mbehou, Mahamat Saleh Daoussa Haggar, Benjamin Mampassi
AppliedMath
Vector-borne diseases pose a significant public health challenge in tropical regions, where complex interactions between hosts, vectors, and the environment drive epidemic dynamics. In this study, we develop a spatio-temporal mathematical model to describe the spread of such diseases, incorporating population dynamics and spatial–temporal factors affecting pathogen transmission. We conduct a theoretical analysis of the model, proving the existence, uniqueness, and positivity of solutions. Additionally, we examine equilibrium states and key epidemiological parameters, including the basic reproduction number. Our findings provide mathematical insights into epidemic propagation and offer a foundation for designing effective control strategies.
SSRN Electronic Journal
SSRN Electronic Journal
S. Dawe, Mahamat Saleh Daoussa Haggar, L.M. Kemfouet Tsopze, M. Mbehou
Partial Differential Equations in Applied Mathematics
We investigate the convergence properties Crank–Nicolson scheme coupled with the finite element approximation of the Fitzhugh–Nagumo system. This model describes the dynamics of excitable media, such as nerve cells, and has applications in various fields, including neuroscience and cardiac modeling. The study focuses on the time splitting algorithm, which combines implicit time-stepping using Crank–Nicolson with piecewise finite element spatial discretization. The well-posedness and error estimates for both the temporal and fully discretization errors are established. This type of boundary conditions are incorporated into the formulation, allowing for non-homogeneous fluxes at the domain boundaries. Numerical experiments validate the theoretical findings.
Mahamat Saleh Daoussa Haggar, M. Mbehou, Abdou Njifenjou
Journal of Mathematics and Computer Science
A theoretical analysis of a Crank-Nicolson Galerkin finite element method for a class of nonlinear nonlocal diffusion problems associated with p -Laplace-type operator is presented here. It is shown, by a rigorous analysis that the unconditionally optimal error estimates for the fully discrete scheme are established. The presence of the nonlocal term in the models destroys the sparsity of the Jacobian matrices when solving the problem numerically using finite element method and Newton-Raphson method. As a consequence, computations consume more time and space in contrast to local problems. To overcome this difficulty, a new algorithm is proposed to avoid the full Jacobian matrix. Finally, some numerical simulations are presented to illustrate our theoretical analysis.
Mahamat Saleh Daoussa Haggar, M. Mbehou
Arab Journal of Mathematical Sciences
Purpose This paper focuses on the unconditionally optimal error estimates of a linearized second-order scheme for a nonlocal nonlinear parabolic problem. The first step of the scheme is based on Crank–Nicholson method while the second step is the second-order BDF method. Design/methodology/approach A rigorous error analysis is done, and optimal L 2 error estimates are derived using the error splitting technique. Some numerical simulations are presented to confirm the study’s theoretical analysis. Findings Optimal L 2 error estimates and energy norm. Originality/value The goal of this research article is to present and establish the unconditionally optimal error estimates of a linearized second-order BDF finite element scheme for the reaction-diffusion problem. An optimal error estimate for the proposed methods is derived by using the temporal-spatial error splitting techniques, which split the error between the exact solution and the numerical solution into two parts, that is, the temporal error and the spatial error. Since the spatial error is not dependent on the time step, the boundedness of the numerical solution in L∞-norm follows an inverse inequality immediately without any restriction on the grid mesh.
M. Mbehou, Mahamat Saleh Daoussa Haggar, P. M. Tchepmo Djomegni
Scientific African
This paper is devoted to the analysis of the finite element method for the mixed problem for the Kirchhoff nonlinear model given by the hyperbolic-parabolic equations in a bounded noncylindrical domain with moving boundaries. With the use of the coordinate transformation which fixes the boundaries, the semidiscrete formulation is presented and the convergence and error bounds in the energy norm and for the first order derivative with respect to time in the L2-norm are established. In particular, the error in the energy norm and for the first order derivative with respect to time in the L2-norm is shown to converge with the optimal order O(hr) with respect to the mesh size h and the polynomial degree r≥1. To obtain the fully discrete solution, the generalized-α method is adapted to the semidiscrete formulation. The test problems used are designed to illustrate the behavior of the algorithms. Some numerical tests using Matlab are performed to confirm our theoretical findings.
Gabriel Deugoué, J.K. Djoko, Virginie S. Konlack, M. Mbehou
Journal of Scientific Computing
P. M. Tchepmo Djomegni, Emile Franc Doungmo Goufo, Subrata Kumar Sahu, M. Mbehou
Natural Resource Modeling
Numerical Analysis and Applications
The presence of the nonlocal term in the nonlocal problems destroys the sparsity of the Jacobian matrices when solving the problem numerically using finite elementmethod and Newton–Raphson method. As a consequence, computations consume more time and space in contrast to local problems. To overcome this difficulty, this paper is devoted to the analysis of a linearized theta-Galerkin finite element method for the time-dependent nonlocal problem with nonlinearity of Kirchhoff type. Hereby, we focus on time discretization based on θ -time stepping scheme with θ ∈ [½, 1). Some error estimates are derived for the standard Crank–Nicolson ( θ = ½), the shifted Crank–Nicolson ( θ = ½ + δ , where δ is the time-step) and the general case ( θ ≠ ½ + kδ , where k = 0, 1). Finally, numerical simulations that validate the theoretical findings are exhibited.
Emile Franc Doungmo Goufo, M. Mbehou, Morgan M. Kamga Pene
Chaos Solitons & Fractals
J.K. Djoko, Virginie Konlack Socgnia, M. Mbehou
Computers & Mathematics with Applications
Mathematical Methods in the Applied Sciences
This paper is devoted to the analysis of a linearized theta‐Galerkin finite element method for the time‐dependent coupled systems resulting from microsensor thermistor problems. Hereby, we focus on time discretization based on θ ‐time stepping scheme with including the standard Crank‐Nicolson ( ) and the shifted Crank‐Nicolson ( , where δ is the time‐step) schemes. The semidiscrete formulation in space is presented and optimal error bounds in L 2 ‐norm and the energy norm are established. For the fully discrete system, the optimal error estimates are derived for the standard Crank‐Nicolson, the shifted Crank‐Nicolson, and the general case where with k =0,1 . Finally, numerical simulations that validate the theoretical findings are exhibited.
M. Mbehou, R. Maritz, P.M.D. Tchepmo
East Asian Journal on Applied Mathematics
Abstract This article is devoted to the study of the finite element approximation for a nonlocal nonlinear parabolic problem. Using a linearised Crank-Nicolson Galerkin finite element method for a nonlinear reaction-diffusion equation, we establish the convergence and error bound for the fully discrete scheme. Moreover, important results on exponential decay and vanishing of the solutions in finite time are presented. Finally, some numerical simulations are presented to illustrate our theoretical analysis.
J.K. Djoko, Jean Lubuma, M. Mbehou
Journal of Scientific Computing
J.K. Djoko, M. Mbehou
Journal of Numerical Mathematics
Abstract In this work, we are concerned with the finite element approximation for the stationary power law Stokes equations driven by nonlinear slip boundary conditions of ‘friction type’. After the formulation of the problem as mixed variational inequality of second kind, it is shown by application of a variant of Babuska-Brezzi’s theory for mixed problems that convergence of the finite element approximation is achieved with classical assumptions on the regularity of the weak solution. Next, solution algorithm for the mixed variational problem is presented and analyzed in details. Finally, numerical simulations that validate the theoretical findings are exhibited.
x Introduction 1 0.1 Thesis overview and our contributions . . . . . . . . . . . . . . . . . 4 0.2 Generalities on variational inequality and finite element approximation 5 0.2.1 Function spaces . . . . . . . . . . . . . . . . . . . . . . . . . . 6 0.2.2 Elements of nonlinear analysis . . . . . . . . . . . . . . . . . 9 0.2.3 Standard results on variational inequalities . . . . . . . . . . . 12 0.2.4 Preliminaries on finite element approximations . . . . . . . . . 13 1 Finite element analysis on steady Navier-Stokes and Stokes equations driven by threshold slip boundary conditions 15 1.
J.K. Djoko, M. Mbehou
UpSpace Institutional Repository (University of Pretoria)
This paper is devoted to the study of finite element approximations of variational \ninequalities with a special nonlinearity coming from boundary conditions. After re-writing the \nproblems in the form of variational inequalities, a fixed point strategy is used to show existence of \nsolutions. Next we prove that the finite element approximations for the Stokes and Navier Stokes \nequations converge respectively to the solutions of each continuous problems. Finally, Uzawa’s \nalgorithm is formulated and convergence of the procedure is shown, and numerical validation test \nis achieved.
H. Oleï Tahar, Mahamat Saleh Daoussa Haggar, M. Mbehou
Results in Applied Mathematics
This article concerns the numerical approximation of the two-dimensional nonstationary Navier–Stokes equations with slip boundary conditions of friction type. It studies the well-posedness and error analysis properties of the numerical scheme in L2-norm for all positive time using the two-step backward differentiation formula (BDF) in time and the finite element approximation in space. Error estimates are proved under feasible assumptions on the regularity of the solution and with the aid of different versions of discrete Grownwall lemmas. Finally, some numerical simulations are presented to illustrate our theoretical analysis.
M. Mbehou, Mahamat Saleh Daoussa Haggar, H. Oleï Tahar
Journal of Applied Mathematics
This paper is devoted to the study of numerical approximation for a class of two-dimensional Navier-Stokes equations with slip boundary conditions of friction type. The objective is to establish the well-posedness and stability of the numerical scheme in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"> <a:msup> <a:mrow> <a:mi>L</a:mi> </a:mrow> <a:mrow> <a:mn>2</a:mn> </a:mrow> </a:msup> </a:math> -norm and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" id="M2"> <c:msup> <c:mrow> <c:mi>H</c:mi> </c:mrow> <c:mrow> <c:mn>1</c:mn> </c:mrow> </c:msup> </c:math> -norm for all positive time using the Crank-Nicholson scheme in time and the finite element approximation in space. The resulting variational structure dealing with is in the form of inequality, and obtaining <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" id="M3"> <e:msup> <e:mrow> <e:mi>H</e:mi> </e:mrow> <e:mrow> <e:mn>1</e:mn> </e:mrow> </e:msup> </e:math> -estimate is more involved because of the presence of the nondifferentiable term appearing at the boundary where slip occurs. We prove that the numerical scheme is stable in <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" id="M4"> <g:msup> <g:mrow> <g:mi>L</g:mi> </g:mrow> <g:mrow> <g:mn>2</g:mn> </g:mrow> </g:msup> </g:math> and <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" id="M5"> <i:msup> <i:mrow> <i:mi>H</i:mi> </i:mrow> <i:mrow> <i:mn>1</i:mn> </i:mrow> </i:msup> </i:math> -norms with the aid of different versions of discrete Grownwall lemmas, under a CFL-type condition. Finally, some numerical simulations are presented to illustrate our theoretical analysis.
J.K. Djoko, Jonas Koko, M. Mbehou, Toni Sayah
Computers & Mathematics with Applications
Kamdem, Djoko, Jonas Koko, M. Mbehou, Toni Sayah
HAL (Le Centre pour la Communication Scientifique Directe)
Antoine-Marie Bogso, M. Mbehou
arXiv (Cornell University)
Given a family $(μ_λ,λ\geq0)$ of integrable mean-zero probability measures such that, for every $λ\geq0$, $μ_λ$ is the image of $μ_1$ under the homothety $y\longmapsto\sqrtλy$, we provide a necessary and sufficient condition on $μ_1$ under which the Root embedding algorithm yields a self-similar martingale with one-dimensional marginals $(μ_λ,λ\geq0)$. Precisely, if $τ_λ$ and $R_λ$ denote the Root solution to the Skorokhod embedding problem (SEP) and the Root regular barrier for $μ_λ$ respectively, then this condition is equivalent to the property that $(R_λ,λ\geq0)$ is non-increasing in the sense of inclusion, which in turn is equivalent to the assertion that $(τ_λ,λ\geq0)$ is non-decreasing a.s. We show that there are many examples for which this result applies and we provide some numerical simulations to illustrate the monotonicity property of regular barriers $(R_λ,λ\geq0)$ in this case.
Jules K. Djoko, Virginie S. Konlack, M. Mbehou
Numerical Methods for Partial Differential Equations
Abstract In this work, we consider the heat equation coupled with Stokes equations under threshold type boundary condition. The conditions for existence and uniqueness of the weak solution are made clear. Next we formulate the finite element problem, recall the conditions of its solvability, and study its convergence by making use of Babuska–Brezzi's conditions for mixed problems. Third we formulate an Uzawa's type iterative algorithm that separates the fluid from heat conduction, study its feasibility, and convergence. Finally the theoretical findings are validated by numerical simulations.
Applicable Analysis
This paper is devoted to the study of the finite element method for a class of non-linear nonlocal diffusion problems associated with p-Laplace-type operator. Using the Euler–Galerkin finite element method, the convergence and a priori error estimates for the semi-discrete as well as fully-discrete formulations are established.
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