相关论文: The DPG-star method
In this paper, we will consider an $hp$-finite elements discretization of a highly indefinite Helmholtz problem by some dG formulation which is based on the ultra-weak variational formulation by Cessenat and Depr\'{e}s. We will introduce an…
The DPG method with optimal test functions for solving linear quadratic optimal control problems with control constraints is studied. We prove existence of a unique optimal solution of the nonlinear discrete problem and characterize it…
A discontinuous Petrov-Galerkin (DPG) method is used to solve the time-harmonic equations of linear viscoelasticity. It is based on a "broken" primal variational formulation, which is very similar to the classical primal variational…
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 present a new $hp$-version space-time discontinuous Galerkin (dG) finite element method for the numerical approximation of parabolic evolution equations on general spatial meshes consisting of polygonal/polyhedral (polytopic) elements,…
Discontinuous Petrov-Galerkin (DPG) methods are new discontinuous Galerkin methods with interesting properties. In this article we consider a domain decomposition preconditioner for a DPG method for the Poisson problem.
A new finite element method with discontinuous approximation is introduced for solving second order elliptic problem. Since this method combines the features of both conforming finite element method and discontinuous Galerkin (DG) method,…
We consider a model convection-diffusion problem and present useful connections between the finite differences and finite element discretization methods. We introduce a general upwinding Petrov-Galerkin discretization based on bubble…
We introduce a new discretization based on the Trefftz-DG method for solving the Stokes equations. Discrete solutions of a corresponding method fulfill the Stokes equation pointwise within each element and yield element-wise divergence-free…
This paper presents a new $L^p$-primal-dual weak Galerkin (PDWG) finite element method for the div-curl system with the normal boundary condition for $p>1$. Two crucial features for the proposed $L^p$-PDWG finite element scheme are as…
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 present recent finite element numerical results on a model convection-diffusion problem in the singular perturbed case when the convection term dominates the problem. We compare the standard Galerkin discretization using the linear…
We introduce a cousin of the DPG method - the DPG* method - discuss their relationship and compare the two methods through numerical experiments.
In this article, we employ the construction of the time-marching Discontinuous Petrov-Galerkin (DPG) scheme we developed for linear problems to derive high-order multistage DPG methods for non-linear systems of ordinary differential…
In this paper, the authors devise a new discretization scheme for div-curl systems defined in connected domains with heterogeneous media by using the weak Galerkin finite element method. Two types of boundary value problems are considered…
The proximal Galerkin finite element method is a high-order, low-iteration complexity, nonlinear numerical method that preserves the geometric and algebraic structure of point-wise bound constraints in infinite-dimensional function spaces.…
A finite element methodology for large classes of variational boundary value problems is defined which involves discretizing two linear operators: (1) the differential operator defining the spatial boundary value problem; and (2) a Riesz…
We introduce a max-plus analogue of the Petrov-Galerkin finite element method to solve finite horizon deterministic optimal control problems. The method relies on a max-plus variational formulation. We show that the error in the sup norm…
A general analysis framework is presented in this paper for many different types of finite element methods (including various discontinuous Galerkin methods). For second order elliptic equation, this framework employs $4$ different…
We propose a novel framework of generalised Petrov-Galerkin Dynamical Low Rank Approximations (DLR) in the context of random PDEs. It builds on the standard Dynamical Low Rank Approximations in their Dynamically Orthogonal formulation. It…