A priori and a posteriori error analysis for a large-scale ocean circulation finite element model

2003 ◽  
Vol 192 (51-52) ◽  
pp. 5305-5327 ◽  
Author(s):  
J.M. Cascón ◽  
G.C. Garcı́a ◽  
R. Rodrı́guez
Keyword(s):  
Finite Element ◽  
Ocean Circulation ◽  
Large Scale ◽  
A Priori ◽  
Element Model ◽  
Posteriori Error ◽  
A Posteriori ◽  
A Posteriori Error Analysis ◽  
A Posteriori Error ◽  
Posteriori Error Analysis

Unified a Priori Error Estimate and a Posteriori Error Estimate of CIP-FEM for Elliptic Equations

2016 ◽  
Vol 8 (4) ◽  
pp. 517-535
Author(s):  
Jianye Wang ◽  
Rui Ma
Keyword(s):  
Finite Element ◽  
Error Analysis ◽  
Error Estimate ◽  
A Priori ◽  
Posteriori Error ◽  
A Posteriori ◽  
A Posteriori Error Analysis ◽  
A Posteriori Error ◽  
Penalty Term ◽  
Posteriori Error Analysis

AbstractThis paper is devoted to a unified a priori and a posteriori error analysis of CIP-FEM (continuous interior penalty finite element method) for second-order elliptic problems. Compared with the classic a priori error analysis in literature, our technique can easily apply for any type regularity assumption on the exact solution, especially for the case of lowerH1+sweak regularity under consideration, where 0 ≤s≤ 1/2. Because of the penalty term used in the CIP-FEM, Galerkin orthogonality is lost and Céa Lemma for conforming finite element methods can not be applied immediately when 0≤s≤1/2. To overcome this difficulty, our main idea is introducing an auxiliaryC1finite element space in the analysis of the penalty term. The same tool is also utilized in the explicit a posteriori error analysis of CIP-FEM.

Sign in / Sign up

Export Citation Format

Share Document