Certain results of numerical simulations obtained by the use of the spectral finite element method in time domain are presented by the authors. They were selected in order to show the effectiveness of the spectral finite element method for investigation of problems associated with propagation of guided elastic waves in a wind turbine laminated composite blade. Results of these simulations were ...

In this study, a hp-version of Finite Element Method (FEM) was applied for forward modeling in image reconstruction of Electrical Impedance Tomography (EIT). The EIT forward solver is normally based on the conventional Finite Element Method (h-FEM). In h-FEM, the polynomial order (p) of the element shape functions is constant and the element size (h) is decreasing. To have an accurate simulatio...

In this paper we combine nonstandard finite-difference (NSFD) schemes and Richardson’s extrapolation method to obtain numerical solutions of two biological systems. The first biological system deals with the dynamics of phytoplankton–nutrient interaction under nutrient recycling and the second one deals with the modeling of whooping cough in the human population. Since both models requires posi...

ADER schemes are numerical methods, which can reach an arbitrary order of accuracy in both space and time. They are based on a reconstruction procedure and the solution of generalized Riemann problems. However, for general boundary conditions, in particular of Dirichlet type, a lack of accuracy might occur if a suitable treatment of boundaries conditions is not properly carried out. In this wor...

In this work, we present a novel method to approximate stiff problems using a finite volume (FV) discretization. The stiffness is caused by the existence of a small parameter in the equation which introduces a boundary layer. The semi-analytic method consists in adding in the finite volume space the boundary layer corrector which encompasses the singularities of the problem. We verify the stabi...

This paper is concerned with a multiscale finite element method for numerically solving second order scalar elliptic boundary value problems with highly oscillating coefficients. In the spirit of previous other works, our method is based on the coupling of a coarse global mesh and of a fine local mesh, the latter one being used for computing independently an adapted finite element basis for the...

We introduce a new class of unfitted finite element methods with high order accurate numerical integration over curved surfaces and volumes which are only implicitly defined by level set functions. An unfitted finite element method which is suitable for the case of piecewise planar interfaces is combined with a parametric mapping of the underlying mesh resulting in an isoparametric unfitted fin...

We propose a numerical method to approximate the solution of second order elliptic problems in nonvariational form. The method is of Galerkin type using conforming finite elements and applied directly to the nonvariational (nondivergence) form of a second order linear elliptic problem. The key tools are an appropriate concept of “finite element Hessian” and a Schur complement approach to solvin...

We discuss a priori error estimates for a semidiscrete piecewise linear finite volume element (FVE) approximation to a second order wave equation in a two-dimensional convex polygonal domain. Since the domain is convex polygonal, a special attention has been paid to the limited regularity of the exact solution. Optimal error estimates in L2, H1 norms and quasioptimal estimates in L∞ norm are di...