Boniface Nkemzi

• Professor
• Head of Department at University of Buea

Solutions of boundary value problems for linear partial differential equations are known to exhibit singular behaviors near the boundary of nonsmooth domains. In this case, one is usually interested on the asymptotic behavior of the solutions near the geometric singularities. However, for both mathematical and engineering purposes, it is important...

Solutions of boundary value problems in three‐dimensional domains with edges may exhibit singularities which are known to influence both the accuracy of the finite element solutions and the rate of convergence in the error estimates. This paper considers boundary value problems for the Poisson equation on typical domains Ω ⊂ ℝ³ with edge singularit...

The overall efficiency and accuracy of standard finite element methods may be severely reduced if the solution of the boundary value problem entails singularities. In the particular case of time-harmonic Maxwell’s equations in nonconvex polygonal domains Ω, H1-conforming nodal finite element methods may even fail to converge to the physical solutio...

In N kemzi and Jung 2013 explicit extraction formulas for the computation of the edge flux intensity functions for the Laplacian at axisymmetric edges are presented. The present paper proposes a new adaptation for the Fourier-finite-element method for efficient numerical treatment of boundary value problems for the Poisson equation in axisymmetric...

We consider boundary value problems for the Poisson equation on polygonal domains with general nonhomogeneous mixed boundary conditions and derive, on the one hand, explicit extraction formulas for the coefficients of the singularities. On the other hand, the formulas are used to construct efficient adaptations for the $ h $-, $ p $- and $ hp $-ver...

The solution fields of Maxwell’s equations are known to exhibit singularities near corners, crack tips, edges, and so forth of the physical domain. The structures of the singular fields are well known up to some undetermined coefficients. In two-dimensional domains with corners and cracks, the unknown coefficients are real constants. However, in th...

We present a new finite element algorithm for computing the stress intensity factors and the solution of boundary value problems for the Poisson equation in two-dimensional domains with corners. The method makes use of an explicit expression for the stress intensity factors in terms of the function of the right hand side, the solution of the bounda...

We present explicit representation formulas for the coefficients of the singularities associated with mixed boundary value problems for the Poisson equation in two-dimensional domains with corners and three-dimensional domains with straight edges including cracks. We rely on partial Fourier analysis of the boundary value problem in the vicinity of...

Boundary value problems (BVP) in three-dimensional axisymmetric domains can be treated more efficiently by partial Fourier analysis. Partial Fourier analysis is applied to time-harmonic Maxwell's equations in three-dimensional axisymmetric domains with conical points on the rotation axis thereby reducing the three dimensional BVP to an infinite seq...

We present an improved version of the Singular Complement Method (SCM) for Maxwell's equations, which relies on an asymptotic expansion of the solution near non-regular points. This method allows to recover an optimal error estimate when used with P1 Lagrange finite elements; extension to higher-degree elements is possible. It can be applied to sta...

This paper is concerned with the structure of the singular and regular parts of the solution of time-harmonic Maxwell's equations in polygonal plane domains and their effective numerical treatment. The asymptotic behaviour of the solution near corner points of the domain is studied by means of discrete Fourier transformation and it is proved that t...

This paper is concerned with a priori error estimates and convergence analysis of the Fourier-finite-element solutions of the Neumann problem for the Lamé equations in axisymmetric domains with reentrant edges. The Fourier-FEM combines the approximating Fourier method with respect to the rotational angle using trigonometric polynomials of degree...

Three-dimensional time-harmonic Maxwell's problems in axisymmetric domain Ω with edges and conical points on the boundary are treated by means of the Fourier-finite-element method. The Fourier-fem combines the approximating Fourier series expansion of the solution with re-spect to the rotational angle using trigonometric polynomials of degree N (N...

In this paper we present the basic mathematical tools for treating boundary value problems for the Maxwell equations in three-dimensional axisymmetric domains with reentrant edges using the Fourier-finite-element method. We consider both the classical and the regularized time-harmonic Maxwell equations subject to perfect conductor boundary conditio...

This paper analyzes the effects of conical points on the rotation axis of axisymmetric domains Ω^⊂R3 on the regularity of the Fourier coefficients un(n∈Z) of the solution u^ of the Dirichlet problem for the Poisson equation -Δu^=f^ in Ω^. The asymptotic behavior of the coefficients un near the conical points is carefully described and for f^∈L2(Ω^)...

Partial Fourier series expansion is applied to the Dirichlet problem for the Lamé equations in axisymmetric domains ⊂ℝ3 with conical points on the rotation axis. This leads to dimension reduction of the three-dimensional boundary value problem resulting to an infinite sequence of two-dimensional boundary value problems on the plane meridian domain...

This paper is mainly concerned with the structure of the singular and regular parts of the solution of time-harmonic Maxwell's equations in polygonal plane domains. The asymptotic behaviour of the solution near corner points of the domain is studied by means of discrete Fourier transformation. A detailed functional analysis of the solution shows th...

This paper is concerned with the effective implementation of the Fourier-finite-element method, which combines the approximating Fourier and the finite-element methods, for treating the Dirichlet problem for the Lamé equations in axisymmetric domains with conical vertices and reentrant edges. The partial Fourier decomposition reduces the three-dime...

This paper analyses the regularity of the weak solution of the linear elasticity system in three-dimensional axisymmetric domains with reentrant edges under prescribed traction on the boundary by means of Fourier series. Using partial Fourier analysis with respect to one space direction (rotational angle), the three-dimensional boundary value probl...

In this paper, we study the partial Fourier method for treating the Lamé equations in three-­dimensional axisymmetric domains subjected to nonaxisymmetric loads. We consider the mixed boundary value problem of the linear theory of elasticity with the displacement u, the body force f \in (L_2)^3 and homogeneous Dirichlet and Neumann boundary c...

In this paper, we study the partial Fourier method for treating the Lam'e equations in threedimensional axisymmetric domains subjected to nonaxisymmetric loads. We consider the mixed boundary value problem of the linear theory of elasticity with the displacement u, the body force f 2 (L 2 ) 3 and homogeneous Dirichlet and Neumann boundary condition...

Solutions of elliptic boundary value problems in three-dimensional domains Ω with edges may exhibit singularities. The usual procedure to study these singularities is by the application of the classical Mellin transformation or continuous Fourier transformation. In this paper, we show how the asymp-totic behavior of solutions of elliptic boundary v...