Dr. Behrens-Rincon, Edwin

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.

In this work, we focus our attention in the Stokes flow with nonhomogeneous source terms, formulated in dual mixed form. For the sake of completeness, we begin recalling the corresponding well-posedness at continuous and discrete levels. After that, and with the help of a kind of a quasi-Helmholtz decomposition of functions in H (div), we develop a residual type a posteriori error analysis, deducing an estimator that is reliable and locally efficient. Finally, we provide numerical experiments, which confirm our theoretical results on the a posteriori error estimator and illustrate the performance of the corresponding adaptive algorithm, supporting its use in practice.

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.

This article is concerned with the Stokes system with nonhomogeneous source terms and nonhomogeneous Dirichlet boundary condition. First, we reformulate the problem in its dual mixed form, and then, we study its corresponding well‐posedness. Next, in order to circumvent the well‐known Babuška‐Brezzi condition, we analyze a stabilized formulation of the resulting approach. Additionally, we endow the scheme with an a posteriori error estimator that is reliable and efficient. Finally, we provide numerical experiments that illustrate the performance of the corresponding adaptive algorithm and support its use in practice.

One of the most time-consuming activities in higher education is reviewing and grading student evaluations. Rapid and effective feedback of evaluations, along with an appropriate assessment strategy, can significantly improve students’ performance. Furthermore, academic dishonesty is a major issue in higher education that has been aggravated by the limitations derived from the COVID-19 pandemic. One of the possible ways to mitigate this issue is to give different evaluations to each student, with the negative cost of increasing reviewing time. In this work, an open-source system developed in Python to automatically create and correct evaluations is presented. Using Jupyter Notebook as the graphical user interface, the system allows the creation of individual student question sheets, with the same structure and different parameter values, to send them to students, grade them, and send the final score back to the students. The proposed system requires little programming knowledge for the instructors to use it. The system was applied in Civil Engineering and Geological Engineering programs at the Universidad Católica de la Santísima Concepción, drastically reducing grading time while improving students’ performance.

In this note we describe a strategy that improves the a priori error bounds for augmented mixed methods under appropriate hypotheses. This means that we can derive a priori error estimates for each one of the involved unknowns. Usually, the standard a priori error estimate is for the total error. Finally, a numerical example is included, that illustrates the theoretical results proven in this paper.