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6 papers
A note on devising HDG+ projections on polyhedral elements
Shukai Du, Francisco-Javier Sayas
In this note, we propose a simple way of constructing HDG+ projections on polyhedral elements. The projections enable us to analyze the Lehrenfeld-Schöberl HDG (HDG+) methods in a…
A unified error analysis of HDG methods for the static Maxwell equations
Shukai Du, Francisco-Javier Sayas
We propose a framework that allows us to analyze different variants of HDG methods for the static Maxwell equations using one simple analysis. It reduces all the work to the constr…
An ultraweak formulation of the Reissner-Mindlin plate bending model and DPG approximation
Thomas Führer, Norbert Heuer, Francisco-Javier Sayas
We develop and analyze an ultraweak variational formulation of the Reissner-Mindlin plate bending model both for the clamped and the soft simply supported cases. We prove well-pose…
New analytical tools for HDG in elasticity, with applications to elastodynamics
Shukai Du, Francisco-Javier Sayas
We present some new analytical tools for the error analysis of hybridizable discontinuous Galerkin (HDG) method for linear elasticity. These tools allow us to analyze more variants…
An overlapping decomposition framework for wave propagation in heterogeneous and unbounded media: Formulation, analysis, algorithm, and simulation
Victor Dominguez, Mahadevan Ganesh, Francisco-Javier Sayas
A natural medium for wave propagation comprises a coupled bounded heterogeneous region and an unbounded homogeneous free-space. Frequency-domain wave propagation models in the medi…
A problem in control of elastodynamics with piezoelectric effects
Harbir Antil, Thomas S. Brown, Francisco-Javier Sayas
We consider an optimal control problem where the state equations are a coupled hyperbolic-elliptic system. This system arises in elastodynamics with piezoelectric effects -- the el…