Displaying similar documents to “A multi-space error estimation approach for meshfree methods”

A comparison of some a posteriori error estimates for fourth order problems

Segeth, Karel

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A lot of papers and books analyze analytical a posteriori error estimates from the point of view of robustness, guaranteed upper bounds, global efficiency, etc. At the same time, adaptive finite element methods have acquired the principal position among algorithms for solving differential problems in many physical and technical applications. In this survey contribution, we present and compare, from the viewpoint of adaptive computation, several recently published error estimation procedures...

Regional observation and sensors

Abdelhaq El Jai, Houria Hamzaoui (2009)

International Journal of Applied Mathematics and Computer Science

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The purpose of this short paper is to provide original results related to the choice of the number of sensors and their supports for general distributed parameter systems. We introduce the notion of extended sensors and we show that the observation error decreases when the support of a sensor is widened. We also show that the observation error decreases when the number of sensors increases.

A posteriori error estimation and adaptivity in the method of lines with mixed finite elements

Jan Brandts (1999)

Applications of Mathematics

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We will investigate the possibility to use superconvergence results for the mixed finite element discretizations of some time-dependent partial differential equations in the construction of a posteriori error estimators. Since essentially the same approach can be followed in two space dimensions, we will, for simplicity, consider a model problem in one space dimension.

Guaranteed a-posteriori error estimation for finite element solutions of nonstationary heat conduction problems based on their elliptic reconstructions

Theofanis Strouboulis, Delin Wang (2024)

Applications of Mathematics

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We deal with the a-posteriori estimation of the error for finite element solutions of nonstationary heat conduction problems with mixed boundary conditions on bounded polygonal domains. The a-posteriori error estimates are constucted by solving stationary “reconstruction” problems, obtained by replacing the time derivative of the exact solution by the time derivative of the finite element solution. The main result is that the reconstructed solutions, or reconstructions, are superconvergent...

Goal-oriented error estimates including algebraic errors in discontinuous Galerkin discretizations of linear boundary value problems

Vít Dolejší, Filip Roskovec (2017)

Applications of Mathematics

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We deal with a posteriori error control of discontinuous Galerkin approximations for linear boundary value problems. The computational error is estimated in the framework of the Dual Weighted Residual method (DWR) for goal-oriented error estimation which requires to solve an additional (adjoint) problem. We focus on the control of the algebraic errors arising from iterative solutions of algebraic systems corresponding to both the primal and adjoint problems. Moreover, we present two...