Browsing by Author "Heuer, Norbert"
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- 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 mixed method for Dirichlet problems with radial basis functions(2013) Heuer, Norbert; Thanh, Tran
- 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 Time-Stepping DPG Scheme for the Heat Equation(2017) Führer, Thomas; Heuer, Norbert; Gupta J.
- ItemAdaptive Crouzeix-Raviart boundary element method(2015) Heuer, Norbert; Karkulik, Michael
- ItemAn a posteriori error estimate for a linear-nonlinear transmission problem in plane elastostatics(2002) Barrientos, Mauricio A.; Gatica, Gabriel N.; Heuer, Norbert
- ItemAn additive Schwarz method for the h-p version of the boundary element method for hypersingular integral equations in R-3(2001) Heuer, Norbert; Stephan, Ernst P.
- ItemAn hp-adaptive refinement strategy for hypersingular operators on surfaces(2002) Heuer, Norbert
- ItemAn iterative substructuring method for the hp-version of the BEM on quasi-uniform triangular meshes(2007) Heuer, Norbert; Leydecker, Florian; Stephan, Ernst P.
- ItemAn ultraweak formulation of the Reissner-Mindlin plate bending model and DPG approximation(2020) Führer, Thomas; Heuer, Norbert; Sayas, F. J.
- ItemBoundary integral operators in countably normed spaces(1998) Heuer, Norbert; Stephan, Ernst P.
- ItemConjugate gradient method for dual-dual mixed formulations(2002) Gatica, Gabriel N.; Heuer, Norbert
- ItemDiscontinuous Petrov-Galerkin boundary elements(2017) Heuer, Norbert; Karkulik, Michael
- ItemFully discrete DPG methods for the Kirchhoff-Love plate bending model(2019) Führer, Thomas; Heuer, Norbert
- ItemMortar boundary elements(2010) Healey, Martin; Heuer, Norbert
- ItemNORMAL-NORMAL CONTINUOUS SYMMETRIC STRESSES IN MIXED FINITE ELEMENT ELASTICITY(2024) Carstensen, Carsten; Heuer, Norbert. The classical continuous mixed formulation of linear elasticity with pointwise symmetric stresses allows for a conforming finite element discretization with piecewise polynomials of degree at least three. Symmetric stress approximations of lower polynomial order are only possible when their div-conformity is weakened to the continuity of normal-normal components. In two dimensions, this condition is meant pointwise along edges for piecewise polynomials, but a corresponding characterization for general piecewise H(div) tensors has been elusive. We introduce such a space and establish a continuous mixed formulation of linear planar elasticity with pointwise symmetric stresses that have, in a distributional sense, continuous normal-normal components across the edges of a shape-regular triangulation. The displacement is split into an L2 field and a tangential trace on the skeleton of the mesh. The well-posedness of the new mixed formulation follows with a duality lemma relating the normal-normal continuous stresses with the tangential traces of displacements. For this new formulation we present a lowest-order conforming discretization. Stresses are approximated by piecewise quadratic symmetric tensors, whereas displacements are discretized by piecewise linear polynomials. The tangential displacement trace acts as a Lagrange multiplier and guarantees global div-conformity in the limit as the mesh-size tends to zero. We prove locking-free, quasi-optimal convergence of our scheme and illustrate this with numerical examples.
- ItemNumerical approximation of a time dependent, nonlinear, space-fractional diffusion equation(2007) Ervin, V.; Heuer, Norbert; Roop, J.P.
- ItemON THE COUPLING OF DPG AND BEM(2017) Führer, Thomas; Heuer, Norbert; Karkulik, Michael
- ItemOptimal Quasi-diagonal Preconditioners for Pseudodifferential Operators of Order Minus Two(2019) Führer, Thomas; Heuer, NorbertWe present quasi-diagonal preconditioners for piecewise polynomial discretizations of pseudodifferential operators of order minus two in any space dimension. Here, quasi-diagonal means diagonal up to a sparse transformation. Considering shape regular simplicial meshes and arbitrary fixed polynomial degrees, we prove, for dimensions larger than one, that our preconditioners are asymptotically optimal. Numerical experiments in two, three and four dimensions confirm our results. For each dimension, we report on condition numbers for piecewise constant and piecewise linear polynomials.