The numerical approximation to a parabolic control problem with control and state constraints is studied in this paper. We use standard piecewise linear and continuous finite elements for the space discretization of the state, while the backward Euler method is used for time discretization. A priori error estimates for control and state are obtained by an improved maximum error estimate for cor...

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...

We first propose an adaptive immersed finite element method based on the a posteriori error estimate for solving elliptic equations with non-homogeneous boundary conditions in general Lipschitz domains. The underlying finite element mesh need not fit the boundary of the domain. Optimal a priori error estimate of the proposed immersed finite element method is proved. The immersed finite element ...

Discontinuous Galerkin (DG) finite element methods were studied by many researchers for second-order elliptic partial differential equations, and a priori error estimates were established when the solution of the underlying problem is piecewise H3/2+ smooth with > 0. However, elliptic interface problems with intersecting interfaces do not possess such a smoothness. In this paper, we establish a...

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...

This paper studies the coupling between anisotropic mesh adaptation and goal-oriented error estimate. The former is very well suited to the control of the interpolation error. It is generally interpreted as a local geometric error estimate. On the contrary, the latter is preferred when studying approximation errors for PDEs. It generally involves non local error contributions. Consequently, a f...

Abstract The gradient discretisation method (GDM) is a generic framework designed recently, as in spatial space, to partial differential equations. This paper aims use the GDM establish first general error estimate for numerical approximations of parabolic obstacle problems. gives convergence rates several well-known conforming and non-conforming methods. Numerical experiments based on hybrid f...