scholarly journals An a posteriori error estimate for finite element approximations of a singularly perturbed advection-diffusion problem

1997 ◽  
Vol 87 (2) ◽  
pp. 227-242 ◽  
Author(s):  
Song Wang
Keyword(s):  
Finite Element ◽  
Posteriori Error ◽  
Diffusion Problem ◽  
A Posteriori Error Estimate ◽  
Singularly Perturbed ◽  
Posteriori Error Estimate ◽  
A Posteriori ◽  
A Posteriori Error ◽  
Finite Element Approximations ◽  
Advection Diffusion

A HIERARCHICAL A POSTERIORI ERROR ESTIMATE FOR AN ADVECTION-DIFFUSION-REACTION PROBLEM

2005 ◽  
Vol 15 (07) ◽  
pp. 1119-1139 ◽  
Author(s):  
RODOLFO ARAYA ◽  
ABNER H. POZA ◽  
ERNST P. STEPHAN
Keyword(s):  
Error Estimate ◽  
Posteriori Error ◽  
A Posteriori Error Estimate ◽  
Diffusion Reaction ◽  
Posteriori Error Estimate ◽  
A Posteriori ◽  
A Posteriori Error ◽  
Advection Diffusion ◽  
Norm Of The Error ◽  
Reaction Problem

In this work we introduce a new a posteriori error estimate of hierarchical type for the advection-diffusion-reaction equation. We prove the equivalence between the energy norm of the error and our error estimate using an auxiliary linear problem for the residual and an easy way to prove inf–sup condition.

scholarly journals An adaptive finite element DtN method for the elastic wave scattering by biperiodic structures

2021 ◽  
Author(s):  
Gang Bao ◽  
Xue Jiang ◽  
Peijun Li ◽  
Xiaokai Yuan
Keyword(s):  
Finite Element ◽  
Error Estimate ◽  
Elastic Wave ◽  
Posteriori Error ◽  
A Posteriori Error Estimate ◽  
Posteriori Error Estimate ◽  
Adaptive Finite Element ◽  
A Posteriori ◽  
Truncation Parameter ◽  
A Posteriori Error

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.

Sign in / Sign up

Export Citation Format

Share Document