Data: 6 września 2019 (piątek)
Godz. 13:30
Miejsce: sala 2.41, D.17
Temat: Weak constraint enforcement for stabilized residual minimization methods
Prelegent: Roberto Jesus Cier, Curtin University, Perth, Australia Zachodnia
Abstract:
Standard (Galerkin) finite element methods (FEM) can yield unphysical oscillatory discrete solutions in the convection-dominated regime. We present the weak enforcement of the physical range of values of the solution to overcome the oscillations of a stabilized method. The method combines a residual minimization method for Discontinuous Galerkin (DG) methods stated by Calo et al. [2], nonlinear penalization, based on the previous result of Burman and Ern [1], and, due to the nonlinearity of the penalty term, the nonlinear Discontinuous Petrov-Galerkin (DPG) methodology proposed by Carstensen et al. [3]. The resulting method is a non-conforming DPG scheme where the test space is a discontinuous polynomial space, and the trial space is a subspace of the test space. The main advantage of the residual minimization technique is to provide an error estimate for on-the-fly adaptivity. Numerical examples illustrate the performance of the method.
References:
[1] Calo,V., Ern, A., Muga, I. & Rojas, S. (2019). An adaptive stabilized finite element method based on residual minimization. In preparation.
[2] Burman, E., & Ern, A. (2017). A nonlinear consistent penalty method weakly enforcing positivity in the finite element approximation of the transport equation. Computer Methods in Applied Mechanics and Engineering, 320, 122-132.
[3] Carstensen, C., Bringmann, P., Hellwig, F., & Wriggers, P. (2018). Nonlinear discontinuous Petrov–Galerkin methods. Numerische Mathematik, 139(3), 529-561.