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Recent Advances in Least-Squares and Discontinuous Petrov-Galerkin Finite Element Methods
(De Gruyter, 2019)
© 2019 Walter de Gruyter GmbH, Berlin/Boston 2019.Least-squares (LS) and discontinuous Petrov-Galerkin (DPG) finite element methods are an emerging methodology in the computational partial differential equations with ...
MINRES for Second-Order PDEs with Singular Data
(2022)
Minimum residual methods such as the least-squares finite element method (FEM) or the discontinuous Petrov-Galerkin (DPG) method with optimal test functions usually exclude singular data, e.g., non-square-integrable loads. ...
Uma formulação Petrov-Galerkin descontínuo para solução da equação de Helmholtz com minimização do erro de faseA discontinuous Petrov-Galerkin formulation for Helmholtz equation solution with phase error minimization
(Universidade Federal do Rio de JaneiroBrasilInstituto Alberto Luiz Coimbra de Pós-Graduação e Pesquisa de EngenhariaPrograma de Pós-Graduação em Engenharia CivilUFRJ, 2021)
A robust DPG method for large domains
(2021)
We observe a dramatic lack of robustness of the DPG method when solving problems on large domains and where stability is based on a Poincare-type inequality. We show how robustness can be re-established by using appropriately ...
Trace operators of the bi-Laplacian and applications
(OXFORD UNIV PRESS, 2021)
We study several trace operators and spaces that are related to the bi-Laplacian. They are motivated by the development of ultraweak formulations for the bi-Laplace equation with homogeneous Dirichlet condition, but are ...
DPG Methods for a Fourth-Order div Problem
(2022)
We study a fourth-order div problem and its approximation by the discontinuous Petrov-Galerkin method with optimal test functions. We present two variants, based on first and second-order systems. In both cases, we prove ...
A Discontinuous Petrov–Galerkin Method for Reissner–Mindlin Plates
(2023)
We present a discontinuous Petrov–Galerkin method with optimal test functions for the Reissner–Mindlin plate bending model. Our method is based on a variational formulation that utilizes a Helmholtz decomposition of the ...
Discontinuous Petrov-Galerkin boundary elements
(2017)
Generalizing the framework of an ultra-weak formulation for a hypersingular integral equation on closed polygons in Heuer and Pinochet (SIAM J Numer Anal: 52(6), 2703-2721, 2014), we study the case of a hypersingular ...