Jessika Camaño

Universidad Católica de la Santísima Concepción | UCSC · Departamento de Matemática y Física Aplicadas (DMFA)

This paper deals with high order Whitney forms. We define a canonical isomorphism between two sets of degrees of freedom. This allows to geometrically localize the classical degrees of freedom, the moments, over the elements of a simplicial mesh. With such a localization, it is thus possible to associate, even with moments, a graph structure relati...

A method classically used in the lower polynomial degree for the construction of a finite element basis of the space of divergence-free functions is here extended to any polynomial degree for a bounded domain without topological restrictions. The method uses graphs associated with two differential operators: the gradient and the divergence, and sel...

In this paper, we propose a mass conservative pseudostress-based finite element method for solving the Stokes problem with both Dirichlet and mixed boundary conditions. We decompose the velocity by means of a Helmholtz decomposition and derive a three-field mixed variational formulation, where the pseudostress, the velocity, both in H(div), and an...

In this paper we propose and analyze a new mixed finite element method for a stationary magneto-hydrodynamic (MHD) model. The method is based on the utilization of a new dual-mixed formulation recently introduced for the Navier-Stokes problem, which is coupled with a classical primal formulation for the Maxwell equations. The latter implies that th...

In this paper we develop an a posteriori error analysis of a new momentum conservative mixed finite element method recently introduced for the steady-state Navier–Stokes problem in two and three dimensions. More precisely, by extending standard techniques commonly used on Hilbert spaces to the case of Banach spaces, such as local estimates, and sui...

In this paper, we analyze a divergence‐free finite element method to solve a fluid–structure interaction spectral problem in the three‐dimensional case. The unknowns of the resulting formulation are the fluid and solid displacements and the fluid pressure on the interface separating both media. The resulting mixed eigenvalue problem is approximated...

In this paper, we propose and analyze a new momentum conservative mixed finite element method for the Navier–Stokes problem posed in nonstandard Banach spaces. Our approach is based on the introduction of a pseudostress tensor relating the velocity gradient with the convective term, leading to a mixed formulation where the aforementioned pseudostre...

We propose and analyze an efficient algorithm for the computation of a basis of the space of divergence-free Raviart–Thomas finite elements. The algorithm is based on graph techniques. The key point is to realize that, with very natural degrees of freedom for fields in the space of Raviart–Thomas finite elements of degree \(r+1\) and for elements o...

In the published article, Figure 5 corresponds to an eigenfunction associated not with the first smallest positive eigenvalue. A correct eigenfunction of the latter is depicted in Fig. 1 here. Note that this eigenfunction is axisymmetric, as can be seen from Fig. 2 where its radial, azimuthal and vertical components are plotted on different meridia...

The transmission eigenvalue problem arises in scattering theory. The main difficulty in its analysis is the fact that, depending on the chosen formulation, it leads either to a quadratic eigenvalue problem or to a non-classical mixed problem. In this paper we prove the convergence of a mixed finite element approximation. This approach, which is clo...

In this article, we analyse an augmented mixed finite element method for the steady Navier.Stokes equations. More precisely, we extend the recent results from Cama.no et al.. (2017, Analysis of an augmented mixed-FEM for the Navier.Stokes problem. Math. Comput., 86, 589.615) to the case of mixed no-slip and traction boundary conditions in different...

In this paper we are concerned with two topics: the formulation and analysis of the eigenvalue problem for the \(\mathop {\mathbf {curl}}\nolimits \) operator in a multiply connected domain and its numerical approximation by means of finite elements. We prove that the \(\mathop {\mathbf {curl}}\nolimits \) operator is self-adjoint on suitable Hilbe...

In this paper we analyze the numerical approximation of a saddle-point problem posed in non-standard Banach spaces H(divp, Ω) × Lq(Ω), where H(divp, Ω):= {τ ϵ [L²(Ω)]ⁿ: div τ ϵ Lp(Ω)}, with p > 1 and q ϵ ℝ being the conjugate exponent of p and Ω ⊆ ℝⁿ (n ϵ {2, 3}) a bounded domain with Lipschitz boundary Λ. In particular, we are interested in derivi...

A new stress-based mixed variational formulation for the stationary Navier-Stokes equations with constant density and variable viscosity depending on the magnitude of the strain tensor, is proposed and analyzed in this work. Our approach is a natural extension of a technique applied in a recent paper by some of the authors to the same boundary valu...

We construct sets of basis functions of the space of divergence-free finite elements of Raviart–Thomas type in domains of general topology. Two different methods are presented: one using a suitable selection of the curls of Nédélec finite elements, the other based on an efficient algebraic procedure. The first approach looks to be more useful for n...

The goal of this paper is to compare two computational models for the inverse problem of electroencephalography: the localization of brain activity from measurements of the electric potential on the surface of the head. The source current is modeled as a dipole whose localization and polarization has to be determined. Two methods are considered for...

In this paper we propose and analyze a new augmented mixed finite element method for the Navier-Stokes problem. Our approach is based on the introduction of a "nonlinear-pseudostress" tensor linking the pseudostress tensor with the convective term, which leads to a mixed formulation with the nonlinear-pseudostress tensor and the velocity as the mai...

Electroencephalography is a non-invasive technique for detecting brain activity from the measurement of the electric potential on the head surface. In mathematical terms, it reduces to an inverse problem in which the goal is to determine the source that has generated the electric field from measurements of boundary values of the electric potential....

The three-dimensional eddy current time-dependent problem is considered. We formulate it in terms of two variables, one lying only on the conducting domain and the other on its boundary. We combine finite elements (FEM) and boundary elements (BEM) to obtain a FEM–BEM coupled variational formulation. We establish the existence and uniqueness of the...

We study the inverse source problem for the eddy current approximation of Maxwell equations. As for the full system of Maxwell equations, we show that a volume current source cannot be uniquely identified by knowledge of the tangential components of the electromagnetic fields on the boundary, and we characterize the space of non-radiating sources....