Error analysis of finite element method for Poisson–Nernst–Planck equations

Finite element error analysis of a variational multiscale method for the Navier-Stokes equations

Error analysis of finite element method for Poisson-Nernst-Planck equations

In this paper we study the a priori error estimates of finite element method for the system of time-dependent Poisson–Nernst–Planck equations, and for the first time, we obtain its optimal error estimates in L∞(H1) and L2(H1) norms, and suboptimal error estimates in L∞(L2) norm,with linear element, and optimal error estimates in L∞(L2) norm with quadratic or higher-order element, for both semia...

Solution of Wave Equations Near Seawalls by Finite Element Method

A 2D finite element model for the solution of wave equations is developed. The fluid is considered as incompressible and irrotational. This is a difficult mathematical problem to solve numerically as well as analytically because the condition of the dynamic boundary (Bernoulli’s equation) on the free surface is not fixed and varies with time. The finite element technique is applied to solve non...

Error Analysis of the Finite-Strip Method for Parabolic Equations

The finite-strip method (FSM) is a hybrid technique which combines spectral and finite-element methods. Finite-element approximations are made for each mode of a finite Fourier series expansion. The Galerkin formulated method is set apart from other weighted-residual techniques by the selection of two types of basis functions, a piecewise linear interpolating function and a trigonometric functi...

Error Analysis for an Ale Evolving Surface Finite Element Method

We consider an arbitrary-Lagrangian-Eulerian evolving surface finite element method for the numerical approximation of advection and diffusion of a conserved scalar quantity on a moving surface. We describe the method, prove optimal order error bounds and present numerical simulations that agree with the theoretical results.