Volume 16, Issue 5
A Posteriori Error Analysis of an Augmented Dual-Mixed Method in Linear Elasticity with Mixed Boundary Conditions

Tomás P. Barrios, Edwin M. Behrens & María González

DOI:

Int. J. Numer. Anal. Mod., 16 (2019), pp. 804-824.

Published online: 2019-08

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  • Abstract

We consider an augmented mixed finite element method for the equations of plane linear elasticity with mixed boundary conditions. The method provides simultaneous approximations of the displacements, the stress tensor and the rotation. We develop an a posteriori error analysis based on the Ritz projection of the error and the use of an appropriate auxiliary function, and derive fully local reliable a posteriori error estimates that are locally efficient up to the elements that touch the Neumann boundary. We provide numerical experiments that illustrate the performance of the corresponding adaptive algorithm and support its use in practice.

  • Keywords

a posteriori error estimates, mixed finite element, augmented formulation, stabilization, linear elasticity, Ritz projection.

  • AMS Subject Headings

65N15, 65N30, 65N50, 74B05, 74S05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

tomas@ucsc.cl (Tomás P. Barrios)

ebehrens@ucsc.cl (Edwin M. Behrens)

maria.gonzalez.taboada@udc.es (María González)

  • BibTex
  • RIS
  • TXT
@Article{IJNAM-16-804, author = {Barrios , Tomás P. and Behrens , Edwin M. and González , María }, title = {A Posteriori Error Analysis of an Augmented Dual-Mixed Method in Linear Elasticity with Mixed Boundary Conditions}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2019}, volume = {16}, number = {5}, pages = {804--824}, abstract = {

We consider an augmented mixed finite element method for the equations of plane linear elasticity with mixed boundary conditions. The method provides simultaneous approximations of the displacements, the stress tensor and the rotation. We develop an a posteriori error analysis based on the Ritz projection of the error and the use of an appropriate auxiliary function, and derive fully local reliable a posteriori error estimates that are locally efficient up to the elements that touch the Neumann boundary. We provide numerical experiments that illustrate the performance of the corresponding adaptive algorithm and support its use in practice.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/13255.html} }
TY - JOUR T1 - A Posteriori Error Analysis of an Augmented Dual-Mixed Method in Linear Elasticity with Mixed Boundary Conditions AU - Barrios , Tomás P. AU - Behrens , Edwin M. AU - González , María JO - International Journal of Numerical Analysis and Modeling VL - 5 SP - 804 EP - 824 PY - 2019 DA - 2019/08 SN - 16 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/13255.html KW - a posteriori error estimates, mixed finite element, augmented formulation, stabilization, linear elasticity, Ritz projection. AB -

We consider an augmented mixed finite element method for the equations of plane linear elasticity with mixed boundary conditions. The method provides simultaneous approximations of the displacements, the stress tensor and the rotation. We develop an a posteriori error analysis based on the Ritz projection of the error and the use of an appropriate auxiliary function, and derive fully local reliable a posteriori error estimates that are locally efficient up to the elements that touch the Neumann boundary. We provide numerical experiments that illustrate the performance of the corresponding adaptive algorithm and support its use in practice.

Tomás P. Barrios, Edwin M. Behrens & María González. (2019). A Posteriori Error Analysis of an Augmented Dual-Mixed Method in Linear Elasticity with Mixed Boundary Conditions. International Journal of Numerical Analysis and Modeling. 16 (5). 804-824. doi:
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