Localized pointwise error estimates for mixed finite element methods

Sharply localized pointwise and W∞-1 estimates for finite element methods for quasilinear problems

We establish pointwise andW−1 ∞ estimates for finite element methods for a class of second-order quasilinear elliptic problems defined on domains Ω in Rn. These estimates are localized in that they indicate that the pointwise dependence of the error on global norms of the solution is of higher order. Our pointwise estimates are similar to and rely on results and analysis techniques of Schatz fo...

A new positive definite semi-discrete mixed finite element solution for parabolic equations

In this paper, a positive definite semi-discrete mixed finite element method was presented for two-dimensional parabolic equations. In the new positive definite systems, the gradient equation and flux equations were separated from their scalar unknown equations.  Also, the existence and uniqueness of the semi-discrete mixed finite element solutions were proven. Error estimates were also obtaine...

VARIATIONAL DISCRETIZATION AND MIXED METHODS FOR SEMILINEAR PARABOLIC OPTIMAL CONTROL PROBLEMS WITH INTEGRAL CONSTRAINT

The aim of this work is to investigate the variational discretization and mixed finite element methods for optimal control problem governed by semi linear parabolic equations with integral constraint. The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control is not discreted. Optimal error estimates in L2 are established for the state...

Pointwise localized error estimates for parabolic finite element equations

Pointwise error estimates of the local discontinuous Galerkin method for a second order elliptic problem

In this paper we derive some pointwise error estimates for the local discontinuous Galerkin (LDG) method for solving second-order elliptic problems in RN (N ≥ 2). Our results show that the pointwise errors of both the vector and scalar approximations of the LDG method are of the same order as those obtained in the L2 norm except for a logarithmic factor when the piecewise linear functions are u...