Nitesh Verma, a Doctoral student from the Department of Mathematics of the Indian Institute of Space Science and Technology, IIST, achieved a three months long research stay at the Center for Research in Mathematical Engineering, CI²MA. Her work area is Numerical Analysis of Partial Differential Equations and, during her stay in Concepción, she collaborated with Dr. Raimund Bürger (CI²MA researcher and academician from Universidad de Concepción) and Dr. David Mora (CI²MA researcher and academician from Universidad del Bío-Bío). “I studied my grade in Mumbai and then I post-graduated at Delhi University, both in India. And, since 2016, I am working at IIST and my research adviser is Dr. Sarvesh Kumar. Here at CI²MA, I worked with Dr. Bürger, Dr. Mora and also collaborate with Dr. Ricardo Ruiz-Baier from Oxford. These weeks, we all worked on poro-elasticity problems and sedimentation problems. And nearly coupled problems were also seen”, she explains.

Nitesh also highlighted CI²MA excellent scientific and human environment. “Everybody is so friendly here, so it has been easy for me to work, to focus and not having any distractions while working. And CI²MA Professors have been all the time available for me to clear any doubt. I really enjoyed being part of it. I also had the chance to stay with Yolanda Vásquez, in her apartment, during my stay. That allowed me to talk to someone who is foreigner just like me, but who also works at CI²MA”. About the references she had about CI²MA, previously to her visit, Nitesh explains that Professors Ruiz-Baier and Kumar permanently work together and that it is how the idea of she achieving a research stay in Concepción originated. “My guide at the IIST came here in 2014 for some collaboration, and I also met Sudarshan Kumar who made a postdoc stay here. That’s how all started. And this year, according to the progress of my research I needed a specific help that Professor David Mora could provide”, she explains. In addition, Bürger comments that “the formation of young generations of mathematicians is at the core of international collaborations, even over very long distances, and the formation of new contacts is to the benefit of both parties. I am grateful that Nitesh’s visit has been made possible, especially through the support by her advisor, Sarvesh Kumar, who had received me in January 2019. We are looking forward to continuing collaboration with IIST, and are preparing an application for funding collaboration.”  

Among several other activities, Nitesh gave the talk Virtual Element Methods for the Three-Field Formulation of Time-Dependent Linear Poroelasticity in a version of the Seminar on Numerical Analysis and Mathematical Modeling – Graduate (SANMoMa-G), organized by students from Doctoral Program of Applied Sciences with a minor in Mathematical Engineering from UdeC. “It was a virtual element discretization for the numerical approximation of the three-field formulation for poroelasticity introduced in a paper by Professors Oyarzúa (CI²MA and UBB) and Ruiz-Baier (U. of Oxford), with an extension to the case of non-steady problem. An appropriate poroelastic projection operator has been introduced to assist in deriving energy bounds for the time-dependent discrete problem, and optimal a priori error estimates have been established. Numerical verification of the accuracy of the method is conducted through a set of computational tests”, she explained about the presented contents.

Nitesh visit to CI²MA was partially funded by project Fondecyt 1170473 led by Dr. Bürger, and, among other objectives, allow her to finish the paper Advection-diffusion-reaction in poroelastic media. Part I: Well-posedness and discrete analysis co-written with Luis Miguel de Oliveira Vilaca (University of Geneva, Switzerland), Bryan Gómez-Vargas (CI²MA PhD student, by then), Sarvesh Kumar (IIST, India) and Ricardo Ruiz-Baier (U. of Oxford). This paper is currently in pre-print status, and in it, we analyse a PDE system modelling poromechanical processes (formulated in mixed form using the solid deformation, fluid pressure, and total pressure) interacting with diffusing and reacting solutes in the medium. We investigate the well-posedness of the nonlinear set of equations using fixed-point theory, Fredholm’s alternative, a priori estimates, and compactness arguments. We also propose a mixed finite element method and rigorously demonstrate the stability of the scheme”, Nitesh explains.

The IIST

Located in in Kerala, it is an autonomous institution under the Department of Space of Indian government, and its main purpose, since its inauguration in 2017, is to offer high quality education at the undergraduate, graduate, doctoral and post-doctoral levels on areas with special focus to space sciences, space technology and space applications.