A posteriori error analysis of an augmented mixed finite element method for Darcy flow

We develop an a posteriori error analysis of residual type of a stabilized mixed finite element method for Darcy flow. The stabilized formulation is obtained by adding to the standard dual-mixed approach suitable residual type terms arising from Darcy's law and the mass conservation equation. We derive sufficient conditions on the stabilization parameters that guarantee that the augmented variational formulation and the corresponding Galerkin scheme are well-posed. Then, we obtain a simple a posteriori error estimator and prove that it is reliable and locally efficient. Finally, we provide several numerical experiments that illustrate the theoretical results and support the use of the corresponding adaptive algorithm in practice

On an adaptive stabilized mixed finite element method for the Oseen problem with mixed boundary conditions

We consider the Oseen problem with nonhomogeneous Dirichlet boundary conditions on a part of the boundary and a Neumann type boundary condition on the remaining part. Suitable least squares terms that arise from the constitutive law, the momentum equation and the Dirichlet boundary condition are added to a dual-mixed formulation based on the pseudostress- velocity variables. We prove that the new augmented variational formulation and the corresponding Galerkin scheme are well-posed, and a Céa estimate holds for any finite element subspaces. We also provide the rate of convergence when each row of the pseudostress is approximated by Raviart–Thomas elements and the velocity is approximated by continuous piecewise polynomials. We develop an a posteriori error analysis based on a Helmholtz-type decomposition, and derive a posteriori error indicators that consist of two residual terms per element except on those elements with a side on the Dirichlet boundary, where they both have two additional terms. We prove that these a posteriori error indicators are reliable and locally efficient. Finally, we provide several numerical experiments that support the theoretical results. ⃝c 2020TheAuthor(s).PublishedbyElsevierB.V.Thisisanopenaccessarticleundert

Rey–Osterrieth Complex Figure – copy and immediate recall (3 minutes): Normative data for Spanish-speaking pediatric populations

OBJECTIVE: To generate normative data for the Rey–Osterrieth Complex Figure (ROCF) in Spanish-speaking pediatric populations. METHOD: The sample consisted of 4,373 healthy children from nine countries in Latin America (Chile, Cuba, Ecuador, Guatemala, Honduras, Mexico, Paraguay, Peru, and Puerto Rico) and Spain. Each participant was administered the ROCF as part of a larger neuropsychological battery. The ROCF copy and immediate recall (3 minutes) scores were normed using multiple linear regressions and standard deviations of residual values. Age, age2, sex, and mean level of parental education (MLPE) were included as predictors in the analyses. RESULTS: The final multiple linear regression models showed main effect for age on copy and immediate recall scores, such that scores increased linearly as a function of age. Age2 affected ROCF copy score for all countries, except Puerto Rico; and ROCF immediate recall scores for all countries, except Chile, Guatemala, Honduras, Paraguay, and Puerto Rico. Models indicated that children whose parent(s) had a MLPE >12 years obtained higher scores compared to children whose parent(s) had a MLPE≤12 years for Chile, Puerto Rico, and Spain in the ROCF copy, and Paraguay and Spain for the ROCF immediate recall. Sex affected ROCF copy and immediate recall score for Chile and Puerto Rico with girls scoring higher than boys. CONCLUSIONS: This is the largest Spanish-speaking pediatric normative study in the world, and it will allow neuropsychologists from these countries to have a more accurate approach to interpret the ROCF Test in pediatric populations

Low cost a posteriori error estimators for an augmented mixed FEM in linear elasticity. Dedicated to Professor Rodolfo Rodríguez on the occasion of his 60th birthday.

We consider an augmented mixed finite element method applied to the linear elasticity problem and derive a posteriori error estimators that are simpler and easier to implement than the ones available in the literature. In the case of homogeneous Dirichlet boundary conditions, the new a posteriori error estimator is reliable and locally efficient, whereas for non-homogeneous Dirichlet boundary conditions, we derive an a posteriori error estimator that is reliable and satisfies a quasi-efficiency bound. Numerical experiments illustrate the performance of the corresponding adaptive algorithms and support the theoretical results