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Dr. Behrens-Rincon, Edwin
Research Outputs
New a posteriori error estimator for an stabilized mixed method applied to incompressible fluid flows
2019, Barrios-Faundez, Tomas, Behrens-Rincon, Edwin, González, María
We consider an augmented mixed finite element method for incompressible fluid flows and develop a simple a posteriori error analysis. We obtain an a posteriori error estimator that is reliable and locally efficient. We provide numerical experiments that illustrate the performance of the corresponding adaptive algorithm and support its use in practice.
A posteriori error analysis of an augmented dual-mixed method in linear elasticity with mixed boundary conditions
2019, Barrios-Faundez, Tomas, Behrens-Rincon, Edwin, González, María
We consider the augmented mixed finite element method introduced in [7] for the equations of plane linear elasticity with mixed boundary conditions. We develop an a posteriori error analysis based on the Ritz projection of the error and obtain an a posteriori error estimator that is reliable and efficient, but that involves a non-local term. Then, introducing an auxiliary function, we 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.