International Conference on Spectral and High Order Methods
12th - 16th July 2021 | Vienna, Austria
Overview and details of the sessions of this conference. Please select a date or location to show only sessions at that day or location. Please select a single session for detailed view (with abstracts and downloads if available).
Please note that all times are shown in the time zone of the conference. The current conference time is: 1st Dec 2022, 07:33:31am CET
MS 29a: p- and hp-FEM and applications
The aim of this minisymposium is to discuss recent developments and applications of p- and hp-methods
in the context of finite elements, boundary element methods and discontinuous Galerkin methods. It is
very well known that these methods have high convergence properties in terms of the degrees of free-
dom, but they often require specific adaptations in order to ensure their efficiency in terms of computa-
tional costs or their applicability to involved, possibly nonlinear problems. The minisymposium addresses
several topics of p- and hp-methods with a certain focus on algorithmic aspects and covers, for instance,
hp-adaptivity based on error control, numerical integration, fast solvers, implementation aspects (e.g.
evaluation of element matrices) and applications to real world problems (e.g. image based simulations
with more than one billion degrees of freedom).
12:00pm - 12:30pm
Energy based adaptivity in variable-order FEM for linear and nonlinear PDE
University of Bern, Switzerland
We focus on the numerical solution of linear and nonlinear variational PDE, which correspond to the Euler-Lagrange minimization formulation of an associated convex energy functional. We present an iterative minimization technique which allows for the successive adaptive enrichment of an underlying discrete approximation space, without the need of applying a posteriori error estimates. Specifically, we outline a new approach for hp-adaptive FEM employed for the efficient numerical solution of linear and nonlinear second-order elliptic boundary value problems.
12:30pm - 1:00pm
Residual-based a posteriori error estimates for hp-discontinuous Galerkin discretisations of the biharmonic problem
1Inria Paris, Ecole de Ponts; 2University of Vienna; 3University of Nottingham
We introduce a residual-based a posteriori error estimator for a novel hp-version interior penalty discontinuous Galerkin method for the biharmonic problem in two and three dimensions. We prove that the error estimate provides an upper bound and a local lower bound on the error and that the lower bound is robust to the local mesh size but not the local polynomial degree. The suboptimality in terms of the polynomial degree is fully explicit and grows at most algebraically. Our analysis does not require the existence of a $C^1$-conforming piecewise polynomial space and is instead based on an elliptic reconstruction of the discrete solution to the $H^2$ space and a generalised Helmholtz decomposition of the error. This is the first $hp$-version error estimator for the biharmonic problem in two and three dimensions. The practical behaviour of the estimator is investigated through numerical examples in two and three dimensions.
1:00pm - 1:30pm
Error Estimates for hp-FEM in Elastoplasticity
Universität Salzburg, Austria
In this talk we consider a variational inequality formulation as well as a equivalent mixed variational formulation for a model problem in elastoplasticity with linear kinematic hardening and present hp-discretizations for both formulations. We prove that the discrete variational inequality formulation is equivalent to the discrete mixed formulation and show the unique existence of discrete solutions. The main focus is on the derivation of a-priori error estimates and reliable and efficient a-posteriori error estimates. In the end numerical examples in 2D are shown.
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