For a next-nearest neighbour pair interaction model in a periodic domain, a priori and a posteriori analyses of the quasinonlocal quasicontinuum method (QNL-QC) are presented. The results are valid for large deformations and essentially guarantee a one-to-one correspondence between atomistic solutions and QNL-QC solutions. The analysis is based on truncation error and residual estimates in nega...

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...

Adaptive finite element methods for stationary convectiondiffusion problems are designed and analyzed. The underlying discretization scheme is the Shock-capturing Streamline Diffusion method. The adaptive algorithms proposed are based on a posteriori error estimates for this method leading to reliable methods in the sense that the desired error control is guaranteed. A priori error estimates ar...

We got interested in the hypercircle method since it enables the derivation of reliable a posteriori error estimates without generic constants. It turned out, however, that it avoids also a loss of efficiency that we encounter when residual error estimators are used with the hp finite element method. Moreover, we obtain a priori error estimates for the comparison of different finite element fam...

In this paper, we study the finite element method for constrained optimal control problems governed by nonlinear elliptic PDEs. Instead of the standard error estimates under L2or H1norm, we apply the goal-oriented error estimates in order to avoid the difficulties which are generated by the nonsmoothness of the problem. We derive the a priori error estimates of the goal function, and the error ...

Under some conditions on f(u), we show that for small, the only solutions to the following elliptic equation u ? u + f(u) = 0 in ; u > 0 in ; @u @ = 0 on @ are constants, provided that R 3 is convex. The proof only uses integration by parts.

In this paper, we consider a priori and posteriori error estimates of the H (curl 2 )-conforming finite element when solving quad-curl eigenvalue problem. An estimate eigenvalues with convergence order 2( s − 1) is obtained if corresponding eigenvector u ∈ 1 (Ω) ∇ × (Ω). For estimate, by analyzing associated source problem, obtain lower upper bounds for errors eigenvectors in energy norm eigenv...