Enrique Otarola
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Research Interests
Enrique Otarola has a total of 51 co-authors. Here are the top co-authors by number of shared publications:
- Abner J. Salgado
Department of Mathematics University of Tennessee 37996 Knoxville TN USA
42 shared publications - Alejandro Allendes
Departamento de Matemática, Universidad Técnica Federico Santa Mariá, Valparaiso, Chile
16 shared publications - Daniel Quero
Departamento de Matemática Universidad Técnica Federico Santa María Valparaíso Chile
12 shared publications - Ricardo H. Nochetto
University of Maryland
12 shared publications - Francisco Fuica
Departamento de Matemática Universidad Técnica Federico Santa María Valparaíso Chile
10 shared publications - Harbir Antil
George Mason University
10 shared publications
Latest Publications
- Open Access
The spectral fractional Laplacian with measure valued right hand sides: analysis and approximation
We consider the spectral definition of the fractional Laplace operator and study a basic linear problem involving this operator and singular forcing. In two dimensions, we introduce an appropriate weak formulation in fractional Sobolev spaces and prove that it is well-posed. As an application of these results, we analyze a pointwise tracking optimal control problem for fractional diffusion. We also develop a finite element scheme for the linear problem using continuous, piecewise linear functions, prove a convergence result in energy norm, and derive an error bound in $L^2(Ω)$. Finally, we propose a practical scheme based on a diagonalization technique and derive an error bound in $L^2(Ω)$ using a regularization argument.Open AccessThe spectral fractional Laplacian with measure valued right hand sides: analysis and approximation
We consider the spectral definition of the fractional Laplace operator and study a basic linear problem involving this operator and singular forcing. In two dimensions, we introduce an appropriate weak formulation in fractional Sobolev spaces and prove that it is well-posed. As an application of these results, we analyze a pointwise tracking optimal control problem for fractional diffusion. We also develop a finite element scheme for the linear problem using continuous, piecewise linear functions, prove a convergence result in energy norm, and derive an error bound in $L^2(Ω)$. Finally, we propose a practical scheme based on a diagonalization technique and derive an error bound in $L^2(Ω)$ using a regularization argument. - Open Access
A bilinear pointwise tracking optimal control problem for a semilinear elliptic PDE
We consider a bilinear optimal control problem with pointwise tracking for a semilinear elliptic PDE in two and three dimensions. The control variable enters the PDE as a (reaction) coefficient and the cost functional contains point evaluations of the state variable. These point evaluations lead to an adjoint problem with a linear combination of Dirac measures as a forcing term. In Lipschitz domains, we derive the existence of optimal solutions and analyze first and necessary and sufficient second order optimality conditions. We also prove that every locally optimal control $\bar u$ belongs to $H^1(Ω)$. Finally, assuming that the domain $Ω\subset \mathbb{R}^2$ is a convex polygon, we prove that $\bar u \in C^{0,1}(\bar Ω)$.Open AccessA bilinear pointwise tracking optimal control problem for a semilinear elliptic PDE
We consider a bilinear optimal control problem with pointwise tracking for a semilinear elliptic PDE in two and three dimensions. The control variable enters the PDE as a (reaction) coefficient and the cost functional contains point evaluations of the state variable. These point evaluations lead to an adjoint problem with a linear combination of Dirac measures as a forcing term. In Lipschitz domains, we derive the existence of optimal solutions and analyze first and necessary and sufficient second order optimality conditions. We also prove that every locally optimal control $\bar u$ belongs to $H^1(Ω)$. Finally, assuming that the domain $Ω\subset \mathbb{R}^2$ is a convex polygon, we prove that $\bar u \in C^{0,1}(\bar Ω)$. - 24 May 2025
- Published by Springer Nature in Journal of Scientific Computing
- Vol. 104 (1) , 1-33
Finite Element Approximation for A Convective Brinkman–Forchheimer Problem Coupled with A Heat Equation
- 24 May 2025
- Published by Springer Nature in Journal of Scientific Computing
- Vol. 104 (1) , 1-33
Finite Element Approximation for A Convective Brinkman–Forchheimer Problem Coupled with A Heat Equation
- 22 January 2025
- Published by Springer Nature in Applied Mathematics & Optimization
- Vol. 91 (1) , 1-32
Fractional, Semilinear, and Sparse Optimal Control: A Priori Error Bounds
- 22 January 2025
- Published by Springer Nature in Applied Mathematics & Optimization
- Vol. 91 (1) , 1-32
Fractional, Semilinear, and Sparse Optimal Control: A Priori Error Bounds
- Open Access
A virtual element method for a convective Brinkman-Forchheimer problem coupled with a heat equation
We develop a virtual element method to solve a convective Brinkman-Forchheimer problem coupled with a heat equation. This coupled model may allow for thermal diffusion and viscosity as a function of temperature. Under standard discretization assumptions, we prove the well posedness of the proposed numerical scheme. We also derive optimal error estimates under appropriate regularity assumptions for the solution. We conclude with a series of numerical tests performed with different mesh families that complement our theoretical findings.
Open AccessA virtual element method for a convective Brinkman-Forchheimer problem coupled with a heat equation
We develop a virtual element method to solve a convective Brinkman-Forchheimer problem coupled with a heat equation. This coupled model may allow for thermal diffusion and viscosity as a function of temperature. Under standard discretization assumptions, we prove the well posedness of the proposed numerical scheme. We also derive optimal error estimates under appropriate regularity assumptions for the solution. We conclude with a series of numerical tests performed with different mesh families that complement our theoretical findings.
- 8 August 2024
- Published by Elsevier in Applied Mathematics Letters
- Vol. 158
The linear elasticity system under singular forces
- 8 August 2024
- Published by Elsevier in Applied Mathematics Letters
- Vol. 158
The linear elasticity system under singular forces
- 4 June 2024
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Numerical Analysis
- Vol. 62 (3) , 1344-1371
Bilinear Optimal Control for the Fractional Laplacian: Analysis and Discretization
We adopt the integral definition of the fractional Laplace operator and study an optimal control problem on Lipschitz domains that involves a fractional elliptic PDE as the state equation and a control variable that enters the state equation as a coefficient; pointwise constraints on the control variable are considered as well. We establish the existence of optimal solutions and analyze first- and necessary and sufficient second-order optimality conditions. Regularity estimates for optimal variables are also analyzed. We develop two finite element discretization strategies: a semidiscrete scheme in which the control variable is not discretized and a fully discrete scheme in which the control variable is discretized with piecewise constant functions. For both schemes, we analyze the convergence properties of discretizations and derive error estimates.
- 4 June 2024
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Numerical Analysis
- Vol. 62 (3) , 1344-1371
Bilinear Optimal Control for the Fractional Laplacian: Analysis and Discretization
We adopt the integral definition of the fractional Laplace operator and study an optimal control problem on Lipschitz domains that involves a fractional elliptic PDE as the state equation and a control variable that enters the state equation as a coefficient; pointwise constraints on the control variable are considered as well. We establish the existence of optimal solutions and analyze first- and necessary and sufficient second-order optimality conditions. Regularity estimates for optimal variables are also analyzed. We develop two finite element discretization strategies: a semidiscrete scheme in which the control variable is not discretized and a fully discrete scheme in which the control variable is discretized with piecewise constant functions. For both schemes, we analyze the convergence properties of discretizations and derive error estimates.
- 17 April 2024
- Published by Springer Nature in Journal of Scientific Computing
- Vol. 99 (2) , 1-29
Finite Element Discretizations of a Convective Brinkman–Forchheimer Model Under Singular Forcing
- 17 April 2024
- Published by Springer Nature in Journal of Scientific Computing
- Vol. 99 (2) , 1-29
Finite Element Discretizations of a Convective Brinkman–Forchheimer Model Under Singular Forcing
- Open Access
Numerical discretizations of a convective Brinkman-Forchheimer model under singular forcing
In two-dimensional Lipschitz domains, we analyze a Brinkman--Darcy--Forchheimer problem on the weighted spaces $\mathbf{H}_0^1(ω,Ω) \times L^2(ω,Ω)/\mathbb{R}$, where $ω$ belongs to the Muckenhoupt class $A_2$. Under a suitable smallness assumption, we prove the existence and uniqueness of a solution. We propose a finite element method and obtain a quasi-best approximation result in the energy norm \emph{à la Céa} under the assumption that $Ω$ is convex. We also develop an a posteriori error estimator and study its reliability and efficiency properties. Finally, we develop an adaptive method that yields optimal experimental convergence rates for the numerical examples we perform.Open AccessNumerical discretizations of a convective Brinkman-Forchheimer model under singular forcing
In two-dimensional Lipschitz domains, we analyze a Brinkman--Darcy--Forchheimer problem on the weighted spaces $\mathbf{H}_0^1(ω,Ω) \times L^2(ω,Ω)/\mathbb{R}$, where $ω$ belongs to the Muckenhoupt class $A_2$. Under a suitable smallness assumption, we prove the existence and uniqueness of a solution. We propose a finite element method and obtain a quasi-best approximation result in the energy norm \emph{à la Céa} under the assumption that $Ω$ is convex. We also develop an a posteriori error estimator and study its reliability and efficiency properties. Finally, we develop an adaptive method that yields optimal experimental convergence rates for the numerical examples we perform. - Open Access
Bilinear optimal control for the fractional Laplacian: analysis and discretization
We adopt the integral definition of the fractional Laplace operator and study an optimal control problem on Lipschitz domains that involves a fractional elliptic partial differential equation (PDE) as state equation and a control variable that enters the state equation as a coefficient; pointwise constraints on the control variable are considered as well. We establish the existence of optimal solutions and analyze first and, necessary and sufficient, second order optimality conditions. Regularity estimates for optimal variables are also analyzed. We develop two finite element discretization strategies: a semidiscrete scheme in which the control variable is not discretized, and a fully discrete scheme in which the control variable is discretized with piecewise constant functions. For both schemes, we analyze the convergence properties of discretizations and derive error estimates.
Open AccessBilinear optimal control for the fractional Laplacian: analysis and discretization
We adopt the integral definition of the fractional Laplace operator and study an optimal control problem on Lipschitz domains that involves a fractional elliptic partial differential equation (PDE) as state equation and a control variable that enters the state equation as a coefficient; pointwise constraints on the control variable are considered as well. We establish the existence of optimal solutions and analyze first and, necessary and sufficient, second order optimality conditions. Regularity estimates for optimal variables are also analyzed. We develop two finite element discretization strategies: a semidiscrete scheme in which the control variable is not discretized, and a fully discrete scheme in which the control variable is discretized with piecewise constant functions. For both schemes, we analyze the convergence properties of discretizations and derive error estimates.