An A Posteriori Error Estimator for a Non Homogeneous Dirichlet Problem Considering a Dual Mixed Formulation

Authors

  • T. P. Barrios Associate Professor Universidad Catolica de la Santisima Concepcion, Concepcion, Chile
  • R. Bustinza Universidad de Concepcion, Concepcion, Chile http://orcid.org/0000-0001-6355-8341
  • C. Campos Estudiante tesista Magister en Matematica Aplicada, Universidad Catolica de la Santisima Concepcion, Concepcion, Chile

DOI:

https://doi.org/10.5540/tcam.2022.023.03.00549

Keywords:

mixed finite element methods, a posteriori error estimator, reliability, efficiency

Abstract

In this paper, we describe an a posteriori error analysis for a conforming dual mixed scheme of the Poisson problem with non homogeneous Dirichlet boundary condition. As a result, we obtain an a posteriori error estimator, which is proven to be reliable and locally efficient with respect to the usual norm on H(div;Omega) x L^2(Omega). We remark that the analysis relies on the standard Ritz projection of the error, and take into account a kind of a quasi-Helmholtz decomposition of functions in H(div;Omega), which we have established in this work. Finally, we present one numerical example that validates the well behavior of our estimator, being able to identify the numerical singularities when they exist.

Author Biographies

T. P. Barrios, Associate Professor Universidad Catolica de la Santisima Concepcion, Concepcion, Chile

Departamento de Matematica y Fisica Aplicadas

R. Bustinza, Universidad de Concepcion, Concepcion, Chile

Associate Researcher CI^2MA 

&

Associate Professor

Departamento de Ingenieria Matematica

Facultad de Ciencias Fisicas y Matematicas 

Universidad de Concepcion

C. Campos, Estudiante tesista Magister en Matematica Aplicada, Universidad Catolica de la Santisima Concepcion, Concepcion, Chile

Estudiante tesista Magister en Matematica Aplicada, Universidad Catolica de la Santisima Concepcion

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Published

2022-09-12

How to Cite

Barrios, T. P., Bustinza, R., & Campos, C. (2022). An A Posteriori Error Estimator for a Non Homogeneous Dirichlet Problem Considering a Dual Mixed Formulation. Trends in Computational and Applied Mathematics, 23(3), 549–568. https://doi.org/10.5540/tcam.2022.023.03.00549

Issue

Vol. 23 No. 3 (2022)

Section

Original Article

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