15 citations · 27 across the 7 of their papers we have counts for
8 papers
A high order unfitted hybridizable discontinuous Galerkin method for linear elasticity
Juan M. Cardenas, Manuel Solano
This work analyzes a high order hybridizable discontinuous Galerkin (HDG) method for the linear elasticity problem in a domain not necessarily polyhedral. The domain is approximate…
Afternote to Coupling at a distance: convergence analysis and a priori error estimates
Nestor Sánchez, Tonatiuh Sánchez-Vizuet, Manuel E. Solano
In their article "Coupling at a distance HDG and BEM", Cockburn, Sayas and Solano proposed an iterative coupling of the hybridizable discontinuous Galerkin method (HDG) and the bou…
Error analysis of an unfitted HDG method for a class of non-linear elliptic problems
Nestor Sánchez, Tonatiuh Sánchez-Vizuet, Manuel E. Solano
We study Hibridizable Discontinuous Galerkin (HDG) discretizations for a class of non-linear interior elliptic boundary value problems posed in curved domains where both the source…
A priori and a posteriori error analysis of an unfitted HDG method for semi-linear elliptic problems
Nestor Sánchez, Tonatiuh Sánchez-Vizuet, Manuel E. Solano
We present a priori and a posteriori error analysis of a high order hybridizable discontinuous Galerkin (HDG) method applied to a semi-linear elliptic problem posed on a piecewise…
Adaptive Hybridizable Discontinuous Galerkin discretization of the Grad-Shafranov equation by extension from polygonal subdomains
Tonatiuh Sánchez-Vizuet, Manuel E. Solano, Antoine J. Cerfon
We propose a high-order adaptive numerical solver for the semilinear elliptic boundary value problem modelling magnetic plasma equilibrium in axisymmetric confinement devices. In t…
A Hybridizable Discontinuous Galerkin solver for the Grad-Shafranov equation
Tonatiuh Sánchez-Vizuet, Manuel Solano
In axisymmetric fusion reactors, the equilibrium magnetic configuration can be expressed in terms of the solution to a semi-linear elliptic equation known as the Grad-Shafranov equ…
A superconvergent HDG method for the Maxwell equations
Huangxin Chen, Weifeng Qiu, Ke Shi
We present and analyze a new hybridizable discontinuous Galerkin (HDG) method for the steady state Maxwell equations. In order to make the problem well-posed, a condition of diverg…
A high order HDG method for curved-interface problems via approximations from straight triangulations
Weifeng Qiu, Manuel Solano, Patrick Vega
We generalize the technique of [Solving Dirichlet boundary-value problems on curved domains by extensions from subdomains, SIAM J. Sci. Comput. 34, pp. A497--A519 (2012)] to ellipt…