Residual-based a posteriori error estimate for a mixed Reißner-Mindlin plate finite element method

Consider the scattering of a time-harmonic elastic plane wave by a bi-periodic rigid surface. The displacement of elastic wave motion is modeled by the three-dimensional Navier equation in an unbounded domain above the surface. Based on the Dirichlet-to-Neumann (DtN) operator, which is given as an infinite series, an exact transparent boundary condition is introduced and the scattering problem is formulated equivalently into a boundary value problem in a bounded domain. An a posteriori error estimate based adaptive finite element DtN method is proposed to solve the discrete variational problem where the DtN operator is truncated into a finite number of terms. The a posteriori error estimate takes account of the finite element approximation error and the truncation error of the DtN operator which is shown to decay exponentially with respect to the truncation parameter. Numerical experiments are presented to illustrate the effectiveness of the proposed method.

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A Posteriori Error Estimate of the Theta Time Scheme Combined with a Finite Element Spatial Approximation for Evolutionary HJB Equation with Linear Source Terms

Journal of Computational and Theoretical Nanoscience ◽

10.1166/jctn.2017.6384 ◽

2017 ◽

Vol 14 (2) ◽

pp. 935-946 ◽

Cited By ~ 2

Author(s):

Ali Allahem ◽

Salah Boulaaras ◽

Bahri Cherif

Keyword(s):

Finite Element ◽

Error Estimate ◽

Posteriori Error ◽

A Posteriori Error Estimate ◽

Posteriori Error Estimate ◽

A Posteriori ◽

Source Terms ◽

Linear Source ◽

A Posteriori Error ◽

Spatial Approximation

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A posteriori error estimate for adaptive finite element mesh generation

IEEE Transactions on Magnetics ◽

10.1109/20.43920 ◽

1988 ◽

Vol 24 (1) ◽

pp. 315-317 ◽

Cited By ~ 30

Author(s):

S.-y. Hahn ◽

C. Calmels ◽

G. Meunier ◽

J.L. Coulomb

Keyword(s):

Finite Element ◽

Error Estimate ◽

Mesh Generation ◽

Posteriori Error ◽

A Posteriori Error Estimate ◽

Posteriori Error Estimate ◽

Adaptive Finite Element ◽

A Posteriori ◽

Element Mesh ◽

A Posteriori Error

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A Posteriori Error Analysis for a Lagrange Multiplier Method for a Stokes/Biot Fluid-Poroelastic Structure Interaction Model

Abstract and Applied Analysis ◽

10.1155/2021/8877012 ◽

2021 ◽

Vol 2021 ◽

pp. 1-12

Author(s):

Houédanou Koffi Wilfrid

Keyword(s):

Finite Element ◽

Error Analysis ◽

Error Estimate ◽

Posteriori Error ◽

A Posteriori Error Estimate ◽

Posteriori Error Estimate ◽

A Posteriori ◽

A Posteriori Error Analysis ◽

A Posteriori Error ◽

Posteriori Error Analysis

In this work, we develop an a posteriori error analysis of a conforming mixed finite element method for solving the coupled problem arising in the interaction between a free fluid and a fluid in a poroelastic medium on isotropic meshes in ℝ d , d ∈ 2 , 3 . The approach utilizes a Lagrange multiplier method to impose weakly the interface conditions [Ilona Ambartsumyan et al., Numerische Mathematik, 140 (2): 513-553, 2018]. The a posteriori error estimate is based on a suitable evaluation on the residual of the finite element solution. It is proven that the a posteriori error estimate provided in this paper is both reliable and efficient. The proof of reliability makes use of suitable auxiliary problems, diverse continuous inf-sup conditions satisfied by the bilinear forms involved, Helmholtz decomposition, and local approximation properties of the Clément interpolant. On the other hand, inverse inequalities and the localization technique based on simplexe-bubble and face-bubble functions are the main tools for proving the efficiency of the estimator. Up to minor modifications, our analysis can be extended to other finite element subspaces yielding a stable Galerkin scheme.

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