scholarly journals An Improved a Priori Error Analysis for Finite Element Approximations of Signorini's Problem

2012 ◽  
Vol 50 (5) ◽  
pp. 2400-2419 ◽  
Author(s):  
Patrick Hild ◽  
Yves Renard
Keyword(s):  
Finite Element ◽  
Error Analysis ◽  
A Priori ◽  
Finite Element Approximations ◽  
A Priori Error Analysis ◽  
Signorini's Problem

A Priori Error Analysis for the hp-Version of the Discontinuous Galerkin Finite Element Method for the Biharmonic Equation

2003 ◽  
Vol 3 (4) ◽  
pp. 596-607 ◽  
Author(s):  
Igor Mozolevski ◽  
Endre Süli
Keyword(s):  
Finite Element ◽  
Error Analysis ◽  
Discontinuous Galerkin ◽  
Biharmonic Equation ◽  
A Priori ◽  
Element Approximation ◽  
Main Concern ◽  
Galerkin Finite Element ◽  
A Priori Error Analysis ◽  
Discontinuous Galerkin Finite Element

AbstractWe consider the hp-version of the discontinuous Galerkin finite element approximation of boundary value problems for the biharmonic equation. Our main concern is the a priori error analysis of the method, based on a nonsymmetric bilinear form with interior discontinuity penalization terms. We establish an a priori error bound for the method which is of optimal order with respect to the mesh size h , and nearly optimal with respect to the degree p of the polynomial approximation. For analytic solutions, the method exhibits an exponential rate of convergence under p- refinement. These results are shown in the DG-norm for a general shape regular family of partitions consisting of d-dimensional parallelepipeds. The theoretical results are confirmed by numerical experiments. The method has also been tested on several practical problems of thin-plate-bending theory and has been shown to be competitive in accuracy with existing algorithms.

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