Thc devclopment of hp·version discontinuous Galerkin methods for hyperholic conservalion laws is presented in this work. A priori error estimates are dcrived for a model class of linear hyperbolic conservation laws. These estimates arc obtained using a ncw mesh-dependcnt norm that rel1ects thc dependcnce of the approximate solution on thc local element size and the local order of approximation....

We present a new error analysis for finite element approximations of self-adjoint elliptic eigenvalue problems. The analysis consists of three steps. First we prove a posteriori estimates for the error in the approximate eigenvectors and eigenvalues. The error in the eigenvectors is measured both in the L' and energy norms. In these estimates the error is bounded in terms of the mesh size, a st...

In this paper a priori error analysis for the finite element discretization of an optimal control problem governed by an elliptic state equation is considered. The control variable enters the state equation as a coefficient and is subject to pointwise inequality constraints. We derive a priori error estimates for the discretization error in the control variable and confirm our theoretical resul...

We propose and analyze a new expanded mixed element method, whose gradient belongs to the simple square integrable space instead of the classical H(div; Ω) space of Chen's expanded mixed element method. We study the new expanded mixed element method for convection-dominated Sobolev equation, prove the existence and uniqueness for finite element solution, and introduce a new expanded mixed proje...

In this paper we obtain a priori and a posteriori error estimates for stabilized loworder mixed finite element methods for the Stokes eigenvalue problem. We prove the convergence of the method and a priori error estimates for the eigenfunctions and the eigenvalues. We define an error estimator of the residual type which can be computed locally from the approximate eigenpair and we prove that, u...

We give a relatively complete analysis for the regularization method, which is usually used in solving non-diierentiable minimization problems. The model problem considered in the paper is an obstacle problem. In addition to the usual convergence result and a-priori error estimates, we provide a-posteriori error estimates which are highly desired for practical implementation of the reg-ularizat...