Related papers: A DPG method for shallow shells
We present a discontinuous Petrov-Galerkin (DPG) method with optimal test functions for the Reissner-Mindlin plate bending model. Our method is based on a variational formulation that utilizes a Helmholtz decomposition of the shear force.…
We analyze the discontinuous Petrov-Galerkin (DPG) method with optimal test functions when applied to solve the Reissner-Mindlin model of plate bending. We prove that the hybrid variational formulation underlying the DPG method is…
We consider an elastic model for a circular arch that incorporates membrane, transverse shear, and bending effects. The central line of the arch is partitioned into elements, and an ultra-weak variational formulation is developed alongside…
A spacetime discontinuous Petrov-Galerkin (DPG) method for the linear wave equation is presented. This method is based on a weak formulation that uses a broken graph space. The wellposedness of this formulation is established using a…
We present an anisotropic $hp-$mesh adaptation strategy using a continuous mesh model for discontinuous Petrov-Galerkin (DPG) finite element schemes with optimal test functions, extending our previous work on $h-$adaptation. The proposed…
The discontinuous Petrov-Galerkin method is a minimal residual method with broken test spaces and is introduced for a nonlinear model problem in this paper. Its lowest-order version applies to a nonlinear uniformly convex model example and…
This work represents the first endeavor in using ultraweak formulations to implement high-order polygonal finite element methods via the discontinuous Petrov-Galerkin (DPG) methodology. Ultraweak variational formulations are nonstandard in…
We present an ultra-weak formulation of a hypersingular integral equation on closed polygons and prove its well-posedness and equivalence with the standard variational formulation. Based on this ultra-weak formulation we present a…
We derive and analyze discontinuous Petrov-Galerkin methods with optimal test functions for Signorini-type problems as a prototype of a variational inequality of the first kind. We present different symmetric and non-symmetric formulations…
In this work we give a complete error analysis of the Discontinuous Petrov Galerkin (DPG) method, accounting for all the approximations made in its practical implementation. Specifically, we consider the DPG method that uses a trial space…
We present two new methods for linear elasticity with simultaneously yield stress and displacement approximations of optimal accuracy in both the mesh size h and polynomial degree p. This is achieved within the recently developed…
In this work, we propose and develop an arbitrary-order adaptive discontinuous Petrov-Galerkin (DPG) method for the nonlinear Grad-Shafranov equation. An ultraweak formulation of the DPG scheme for the equation is given based on a minimal…
We study a fourth-order div problem and its approximation by the discontinuous Petrov-Galerkin method with optimal test functions. We present two variants, based on first and second-order systems. In both cases we prove well-posedness of…
We derive an ultraweak variational formulation of the quad-curl problem in two and three dimensions. We present a discontinuous Petrov-Galerkin (DPG) method for its approximation and prove its quasi-optimal convergence. We illustrate how…
We develop and analyze an ultraweak variational formulation for a variant of the Kirchhoff-Love plate bending model. Based on this formulation, we introduce a discretization of the discontinuous Petrov-Galerkin type with optimal test…
We develop and analyze an ultraweak variational formulation of the Reissner-Mindlin plate bending model both for the clamped and the soft simply supported cases. We prove well-posedness of the formulation, uniformly with respect to the…
At the fully discrete setting, stability of the discontinuous Petrov--Galerkin (DPG) method with optimal test functions requires local test spaces that ensure the existence of Fortin operators. We construct such operators for $H^1$ and…
Generalizing the framework of an ultra-weak formulation for a hypersingular integral equation on closed polygons in [N. Heuer, F. Pinochet, arXiv 1309.1697 (to appear in SIAM J. Numer. Anal.)], we study the case of a hypersingular integral…
In this article, several discontinuous Petrov-Galerkin (DPG) methods with perfectly matched layers (PMLs) are derived along with their quasi-optimal graph test norms. Ultimately, two different complex coordinate stretching strategies are…
We develop a discontinuous Petrov-Galerkin scheme with optimal test functions (DPG method) for the Timoshenko beam bending model with various boundary conditions, combining clamped, supported, and free ends. Our scheme approximates the…