High-order/ $$hp$$ -adaptive discontinuous Galerkin finite element methods for acoustic problems

Abstract

Further information on publisher's website:http://dx.doi.org/10.1007/s00607-012-0253-5Publisher's copyright statement:The nal publication is available at Springer via http://dx.doi.org/10.1007/s00607-012-0253-5Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. High-order/hp-adaptive discontinuous Galerkin finite element methods for acoustic problems. Stefano GianiAbstract In this paper we present two different kinds of error estimators for acoustic problems: a residual-based and a dual weighted residual one. The former error estimator is explicit and cheap to compute. The latter is based on a duality argument and it is capable of computing accurate and reliable estimations of quantities of interest, which can be safely used for finite element analysis and model validation. The error estimators presented in this work are designed to work with a hp-adaptive discontinuous Galerkin (DG) methods.

Frequency domain Bernstein-Bézier finite element solver for modelling short waves in elastodynamics

“…It was concluded from these comparative studies that high-order polynomial methods in combination with static condensation are able to deliver comparable or, in some cases, even superior performance. On the other hand, high order hp-discontinuous Galerkin methods have been demonstrated as competitive discretisation schemes (see, e.g., [43,44] and the references cited therein), due to their flexibility in dealing with hp-adaptivity and general shaped elements, and their ability in achieving the exponential convergence rate of spectral techniques.…”

Comparison of continuous and discontinuous Galerkin approaches for variable‐viscosity Stokes flow

“…DG methods are inherently local requiring less communication between neighbouring mesh cells. This facilitates the enforcement of local mass conservation (i.e., per mesh cell) , the development of multiscale methods , ‐adaptivity and parallelization . On the other hand, DG methods yield additional degrees of freedom compared to CG.…”