Displaying similar documents to “A posteriori error estimates for the 3 D stabilized Mortar finite element method applied to the Laplace equation”

Optimal convergence and a posteriori error analysis of the original DG method for advection-reaction equations

Tie Zhu Zhang, Shu Hua Zhang (2015)

Applications of Mathematics

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We consider the original DG method for solving the advection-reaction equations with arbitrary velocity in d space dimensions. For triangulations satisfying the flow condition, we first prove that the optimal convergence rate is of order k + 1 in the L 2 -norm if the method uses polynomials of order k . Then, a very simple derivative recovery formula is given to produce an approximation to the derivative in the flow direction which superconverges with order k + 1 . Further we consider a residual-based...

Adaptive finite element methods for elliptic problems: Abstract framework and applications

Serge Nicaise, Sarah Cochez-Dhondt (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We consider a general abstract framework of a continuous elliptic problem set on a Hilbert space that is approximated by a family of (discrete) problems set on a finite-dimensional space of finite dimension not necessarily included into . We give a series of realistic conditions on an error estimator that allows to conclude that the marking strategy of bulk type leads to the geometric convergence of the adaptive algorithm. These conditions are then verified for different concrete...

Residual  error estimators for contact problems in elasticity

Patrick Hild, Serge Nicaise (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

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This paper is concerned with the unilateral contact problem in linear elasticity. We define two error estimators of residual type to evaluate the accuracy of the mixed finite element approximation of the contact problem. Upper and lower bounds of the discretization error are proved for both estimators and several computations are performed to illustrate the theoretical results.