Browsing by Author "Heuer, Norbert"
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- ItemA direct coupling of local discontinuous Galerkin and bounsary elemt methods(2010) Gatica, Gabriel N.; Heuer, Norbert; Sayas, Francisco Javier
- ItemA Discontinuous Petrov–Galerkin Method for Reissner–Mindlin Plates(2023) Führer, Thomas; Heuer, Norbert; Niemi, Antti H.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 shear force. It produces approximations of the primitive variables and the bending moments. For any canonical selection of boundary conditions the method converges quasi-optimally. In the case of hard-clamped convex plates, we prove that the lowest-order scheme is locking free. Several numerical experiments confirm our results.
- ItemA DPG FRAMEWORK FOR STRONGLY MONOTONE OPERATORS(2018) Cantin, Pierre; Heuer, Norbert
- ItemA DPG method for shallow shells(SPRINGER HEIDELBERG, 2022) Fuhrer, Thomas; Heuer, Norbert; Niemi, Antti H.We develop and analyze a discontinuous Petrov-Galerkin method with optimal test functions (DPG method) for a shallow shell model of Koiter type. It is based on a uniformly stable ultraweak formulation and thus converges robustly quasi-uniformly. Numerical experiments for various cases, including the Scordelis-Lo cylindrical roof, elliptic and hyperbolic geometries, illustrate its performance. The built-in DPG error estimator gives rise to adaptive mesh refinements that are capable to resolve boundary and interior layers. The membrane locking is dealt with by raising the polynomial degree only of the tangential displacement trace variable.
- ItemA dual-dual formulation for the coupling of mixed-FEM and BEM in hyperelasticity(2000) Gatica, Gabriel N.; Heuer, Norbert
- ItemA locking-free DPG scheme for Timoshenko beams(2020) Führer, Thomas; García Vera, Carlos Mauricio; Heuer, Norbert
- ItemA mixed method for Dirichlet problems with radial basis functions(2013) Heuer, Norbert; Thanh, Tran
- ItemA new H(div)-conforming p-interpolation operator in two dimensions(2011) Bespalov, Alexei; Heuer, Norbert
- ItemA Nitsche-based domain decomposition method for hypersingular integral equations(2012) Chouly, Franz; Heuer, Norbert
- ItemA non-symmetric coupling of Boundary Elements with the Hybridizable Discontinuous Galerkin method(2017) Fu, Z.; Heuer, Norbert; Sayas, F.
- ItemA nonconforming domain decomposition approximation for the Helmholtz screen problem with hypersingular operator(2017) Heuer, Norbert; Salmeron Casco, Gredy Jhovanny
- ItemA p-adaptive algorithm for the BEM with the hypersingular operator on the plane screen(2002) Heuer, Norbert; Mellado, Mario E.; Stephan, Ernst P.
- ItemA Posteriori Error Analysis for a Boundary Element Method with Nonconforming Domain Decomposition(2014) Dominguez, Catalina; Heuer, Norbert
- ItemA posteriori error estimates for a mixed-FEM formulation of a non-linear elliptic problem(2002) Araya, Rodolfo; Barrios, Tomás P.; Gatica, Gabriel N.; Heuer, Norbert
- ItemA preconditioned MINRES method for the coupling of mixed-FEM and BEM for some nonlinear problems(2002) Gatica, Gabriel N.; Heuer, Norbert
- ItemA priori and a posteriori error analysis of an augmented mixed finite element method for incompressible fluid flows(2008) Figueroa, Leonardo E.; Gatica, Gabriel N.; Heuer, Norbert
- ItemA residual based a posteriori error estimator for an augmented mixed finite element method in linear elasticity(2006) Barrios, Tomás P.; Gatica, Gabriel N.; González, María; Heuer, Norbert
- ItemA robust DPG method for convection-dominated diffusion problems II : adjoint boundary conditions and mesh-dependent test norms(2014) Chan, J.; Heuer, Norbert; Bui-Thanh, T.; Demkowicz.; L.
- ItemA robust DPG method for large domains(2021) Führer, Thomas; Heuer, NorbertWe 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 scaled test norms. As model cases we study the Poisson problem and the Kirchhoff-Love plate bending model, and also include fully discrete variants where optimal test functions are approximated. Numerical experiments for both model problems, including an-isotropic domains and mixed boundary conditions, confirm our findings.
- ItemA Time-Stepping DPG Scheme for the Heat Equation(2017) Führer, Thomas; Heuer, Norbert; Gupta J.