In this article, we consider rectangular finite element methods for fourth order elliptic singular perturbation problems. We show that the non-C0 rectangular Morley element is uniformly convergent in the energy norm with respect to the perturbation parameter. We also propose a C0 extended high order rectangular Morley element and prove the uniform convergence. Finally, we do some numerical expe...

We propose a fourth-order total bounded variation regularization model which could reduce undesirable effects effectively. Based on this model, we introduce an improved split Bregman iteration algorithm to obtain the optimum solution. The convergence property of our algorithm is provided. Numerical experiments show the more excellent visual quality of the proposed model compared with the second...

omotopy analysis method (ham) is a promising method for handling func-tional equations. recent publications proved the eectiveness of ham in solvingwide variety of problems in dierent elds. ham has a unique property whichmakes it superior to other analytic methods, this property is its ability to con-trol the convergence region of the solution series. in this work, we clari ed theadvantages ...

Third and fourth order convergent methods based on cubic nonpolynomial spline function at midknotes are presented for the numerical solution of a second order two-point boundary value problem with Neumann conditions. Using this spline function a few consistency relations are derived for computing approximations to the solution of the problem. Convergence analysis of these methods is discussed t...

Second and fourth order convergent methods based on Quartic nonpolynomial spline function are presented for the numerical solution of a third order two-point boundary value problem. The proposed approach gives better approximations than existing polynomial spline and finite difference methods and has a lower computational cost. Convergence analysis of the proposed method is discussed; two numer...

We present a numerical solver for the incompressible Navier–Stokes equations that combines fourth-order-accurate discrete approximations and an adaptive tree grid (i.e. h-refinement). The scheme employs novel compact-upwind advection 4th-order accurate projection algorithm whereby solution exactly satisfies incompressibility constraint. Further, we introduce new refinement indicator is tailored...

In this work, we propose staggered FDTD schemes based on the correction function method (CFM) to discretize Maxwell’s equations with embedded perfect electric conductor boundary conditions. The CFM uses a minimization procedure compute given FD scheme in vicinity of retain its order. problem associated approaches is analyzed context boundaries. order obtain well-posed problem, fictitious interf...

SUMMARY We propose the use of high-order weighted essentially non-oscillitory interpolation and moving-least-squares approximation schemes alongside high-order time integration to enable high-order accurate particle-in-cell methods. The key insight is to view the unstructured set of particles as the underlying representation of the continuous fields; the grid used to evaluate integro-differenti...

We consider the numerical evaluation of the Evans function, a Wronskian-like determinant that arises in the study of the stability of travelling waves. Constructing the Evans function involves matching the solutions of a linear ordinary differential equation depending on the spectral parameter. The problem becomes stiff as the spectral parameter grows. Consequently, the Gauss–Legendre method ha...