This paper proves error estimates for H2 conforming finite elements elliptic equations which model the flow of surfaces by different powers mean curvature (this includes flow). The scheme is based on a known regularization procedure and produces kinds errors, error, element discretization regularized problems, full error. While in literature own previous work aspects aforementioned types are tr...

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...

The convergence of waveform relaxation techniques for solving functional-diierential equations is studied. New error estimates are derived that hold under linear and nonlinear conditions for the right-hand side of the equation. Sharp error bounds are obtained under generalized time-dependent Lipschitz conditions. The convergence of the waveform method and the quality of the a priori error bound...

Generalizing an idea from deterministic optimal control, we construct a posteriori error estimates for the spatial discretization error of the stochastic dynamic programming method based on a discrete Hamilton–Jacobi–Bellman equation. These error estimates are shown to be efficient and reliable, furthermore, a priori bounds on the estimates depending on the regularity of the approximate solutio...

A kind of new mixed element method for time-fractional partial differential equations is studied. The Caputo-fractional derivative of time direction is approximated by two-step difference method and the spatial direction is discretized by a new mixed element method, whose gradient belongs to the simple (L (2)(Ω)(2)) space replacing the complex H(div; Ω) space. Some a priori error estimates in L...

We consider a finite element method (FEM) with arbitrary polynomial degree for nonlinear monotone elliptic problems. Using a linear elliptic projection, we first give a new short proof of the optimal convergence rate of the FEM in the L norm. We then derive optimal a priori error estimates in the H and L norm for a FEM with variational crimes due to numerical integration. As an application we d...

A variational approach to derive a piecewise constant conservative approximation of anisotropic diffusion equations is presented. A priori error estimates are derived assuming usual mesh regularity constraints and a posteriori error indicator is proposed and analyzed for the model problem.

This article is concerned with a dual mixed formulation of the Navier-Stokes system in a polygonal domain of the plane with Dirichlet boundary conditions and its numerical approximation. The gradient tensor, a quantity of practical interest, is introduced as a new unknown. The problem is then approximated by a mixed finite element method. Quasi-optimal a priori error estimates are obtained. The...