Error estimates for the finite-element solution of an elliptic singularly perturbed problem

1995 ◽  
Vol 15 (2) ◽  
pp. 161-196 ◽  
Author(s):  
LUTZ ANGERMANN
Keyword(s):  
Finite Element ◽  
Error Estimates ◽  
Singularly Perturbed ◽  
Finite Element Solution ◽  
Singularly Perturbed Problem ◽  
Element Solution

Maximum norm error estimates for Neumann boundary value problems on graded meshes

2018 ◽  
Vol 40 (1) ◽  
pp. 474-497 ◽  
Author(s):  
Thomas Apel ◽  
Sergejs Rogovs ◽  
Johannes Pfefferer ◽  
Max Winkler
Keyword(s):  
Finite Element ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Error Estimates ◽  
Boundary Value ◽  
A Priori ◽  
Neumann Boundary ◽  
Finite Element Solution ◽  
Element Solution ◽  
Polygonal Domains

AbstractThis paper deals with a priori pointwise error estimates for the finite element solution of boundary value problems with Neumann boundary conditions in polygonal domains. Due to the corners of the domain, the convergence rate of the numerical solutions can be lower than in the case of smooth domains. As a remedy, the use of local mesh refinement near the corners is considered. In order to prove quasi-optimal a priori error estimates, regularity results in weighted Sobolev spaces are exploited. This is the first work on the Neumann boundary value problem where both the regularity of the data is exactly specified and the sharp convergence order $h^{2} \lvert \ln h \rvert $ in the case of piecewise linear finite element approximations is obtained. As an extension we show the same rate for the approximate solution of a semilinear boundary value problem. The proof relies in this case on the supercloseness between the Ritz projection to the continuous solution and the finite element solution.

Error estimates for the finite element solution of variational inequalities

1978 ◽  
Vol 31 (1) ◽  
pp. 1-16 ◽  
Author(s):  
Franco Brezzi ◽  
William W. Hager ◽  
P. A. Raviart
Keyword(s):  
Finite Element ◽  
Variational Inequalities ◽  
Error Estimates ◽  
Finite Element Solution ◽  
Element Solution

Error estimates for the finite element solution of variational inequalities

1977 ◽  
Vol 28 (4) ◽  
pp. 431-443 ◽  
Author(s):  
Franco Brezzi ◽  
William W. Hager ◽  
P. A. Raviart
Keyword(s):  
Finite Element ◽  
Variational Inequalities ◽  
Error Estimates ◽  
Finite Element Solution ◽  
Element Solution
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