Browsing by Author "Heuer, Norbert"
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- ItemA balanced finite-element method for an axisymmetrically loaded thin shell(2024) Heuer, Norbert; Linss, TorstenWe analyse a finite-element discretisation of a differential equation describing an axisymmetrically loaded thin shell. The problem is singularly perturbed when the thickness of the shell becomes small. We prove robust convergence of the method in a balanced norm that captures the layers present in the solution. Numerical results confirm our findings.
- ItemA DIRECT COUPLING OF LOCAL DISCONTINUOUS GALERKIN AND BOUNDARY ELEMENT METHODS(2010) Gatica, Gabriel N.; Heuer, Norbert; Javier Sayas, FranciscoThe coupling of local discontinuous Galerkin (LDG) and boundary element methods (BEM), which has been developed recently to solve linear and nonlinear exterior transmission problems, employs a mortar-type auxiliary unknown to deal with the weak continuity of the traces at the interface boundary. As a consequence, the main features of LDG and BEM are maintained and hence the coupled approach benefits from the advantages of both methods. In this paper we propose and analyze a simplified procedure that avoids the mortar variable by employing LDG subspaces whose functions are continuous on the coupling boundary. The continuity can be implemented either directly or indirectly via the use of Lagrangian multipliers. In this way, the normal derivative becomes the only boundary unknown, and hence the total number of unknown functions is reduced by two. We prove the stability of the new discrete scheme and derive an a priori error estimate in the energy norm. A numerical example confirming the theoretical result is provided. The analysis is also extended to the case of nonlinear problems and to the coupling with other discontinuous Galerkin methods.
- ItemA direct coupling of local discontinuous Galerkin and bounsary element 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 DPG method for the quad-curl problem(2023) Fuhrer, Thomas; Herrera, Pablo; Heuer, NorbertWe derive an ultraweak variational formulation of the quad-curl problem in two and three dimensions. We present a discontinuous Petrov-Galerkin (DPG) method for its approximation and prove its quasi-optimal convergence. We illustrate how this method can be applied to the Stokes problem in two dimensions, after an application of the curl operator to eliminate the pressure variable. In this way, DPG techniques known from Kirchhoff-Love plates can be used. We present an a priori error estimate that improves a previous approximation result for effective shear forces by using a less restrictive regularity assumption. Numerical experiments illustrate our findings.
- 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