This note describes an implementation of a discontinuous Petrov Galerkin (DPG) method for acoustic waves within the framework of high order finite elements provided by the software package NGSolve. A technique to impose the impedance boundary condition weakly is indicated. Numerical results from this implementation show that a multiplicative Schwarz algorithm, with no coarse solve, provides a p...

In this work, we derive a goal-oriented a posteriori error estimator for the error due to time discretization. As time discretization scheme we consider the fractional step theta method, that consists of three subsequent steps of the one-step theta method. In every sub-step, the full incompressible system has to be solved (in contrast to time integrators of operator splitting type). The resulti...

Motivated by the Discontinous Petrov-Galerkin method from [Numer. Methods Partial Differential Equations, 27 (2011), 70–105] by Demkowicz and Gopalakrishnan, we study a variational formulation of second order elliptic equations in mixed form, that is obtained by piecewise integrating one of the two equations in the system w.r.t. a partition of the domain into mesh cells. We apply a Petrov-Galer...

The transport and deposition properties of nanoparticles with a range of aerodynamic diameters ( 1 nm ≤ d ≤ 150 nm) were studied for the human airways. A finite element code was developed that solved both the Navier-Stokes and advection-diffusion equations monolithically. When modeling nanoparticle transport in the airways, the finite element method becomes unstable, and, in order resolve this ...

We discuss stabilized Galerkin approximations in a new framework, widening the scope from the usual dichotomy of the discontinuous Galerkin method on the one hand and Petrov– Galerkin methods such as the SUPG method on the other. The idea is to use interior penalty terms as a means of stabilizing the finite element method using conforming or nonconforming approximation, thus circumventing the n...

We introduce a multitree-based adaptive wavelet Galerkin algorithm for space-time discretized linear parabolic partial differential equations, focusing on time-periodic problems. It is shown that the method converges with the best possible rate in linear complexity and can be applied for a wide range of wavelet bases. We discuss the implementational challenges arising from the Petrov-Galerkin n...