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In this paper we propose a new high order accurate space-time DG finite element scheme for the solution of the linear elastic wave equations in first order velocity-stress formulation in two and three-space dimensions on staggered…

Numerical Analysis · Mathematics 2018-05-09 Maurizio Tavelli , Michael Dumbser

This work proposes a superconvergent hybridizable discontinuous Galerkin (HDG) method for the approximation of the Cauchy formulation of the Stokes equation using same degree of polynomials for the primal and mixed variables. The novel…

Numerical Analysis · Mathematics 2019-08-16 Matteo Giacomini , Alexandros Karkoulias , Ruben Sevilla , Antonio Huerta

We prove the contraction property for two successive loops of the adaptive algorithm for the Stokes problem reducing the error of the velocity. The problem is discretized by a divergence-conforming discontinuous Galerkin method which…

Numerical Analysis · Mathematics 2018-07-24 Natasha Sharma , Guido Kanschat

The weak Galerkin (WG) finite element method has shown great potential in solving various type of partial differential equations. In this paper, we propose an arbitrary order locking-free WG method for solving linear elasticity problems,…

Numerical Analysis · Mathematics 2023-11-23 Fuchang Huo , Ruishu Wang , Yanqiu Wang , Ran Zhang

This work develops an energy-based discontinuous Galerkin (EDG) method for the nonlinear Schr\"odinger equation with the wave operator. The focus of the study is on the energy-conserving or energy-dissipating behavior of the method with…

Numerical Analysis · Mathematics 2023-11-14 Kui Ren , Lu Zhang , Yin Zhou

We propose an embedded discontinuous Galerkin (EDG) method to approximate the solution of a distributed control problem governed by convection diffusion PDEs, and obtain optimal a priori error estimates for the state, dual state, their…

Numerical Analysis · Mathematics 2019-06-04 Xiao Zhang , Yangwen Zhang , John R. Singler

In this paper, we present and analyze an interior penalty discontinuous Galerkin method for the distributed elliptic optimal control problems. It is based on a reconstructed discontinuous approximation which admits arbitrarily high-order…

Numerical Analysis · Mathematics 2026-01-05 Ruo Li , Haoyang Liu , Jun Yin

In this paper, we develop a novel enriched Galerkin (EG) method for the steady incompressible Navier-Stokes equations in rotational form, which is both pressure-robust and parameter-free. The EG space employed here, originally proposed in…

Numerical Analysis · Mathematics 2025-11-17 Shuai Su , Xiurong Yan , Qian Zhang

This paper studies pressure-robustness for the axisymmetric Stokes problem. The transformation to cylindrical coordinates requires that the radially weighted velocity is divergence-free in the classical sense. Consequently, traditional…

Numerical Analysis · Mathematics 2026-03-16 Philip L. Lederer , Christoph Lehrenfeld , Christian Merdon , Tim van Beeck

In this paper we establish best approximation type error estimates for the fully discrete Galerkin solutions of the time-dependent Stokes problem using the stream-function formulation. For the time discretization we use the discontinuous…

Numerical Analysis · Mathematics 2026-05-20 Dmitriy Leykekhman , Boris Vexler , Jakob Wagner

Grad-div stabilization is a classical remedy in conforming mixed finite element methods for incompressible flow problems, for mitigating velocity errors that are sometimes called poor mass conservation. Such errors arise due to the…

Numerical Analysis · Mathematics 2019-04-12 Mine Akbas , Alexander Linke , Leo G. Rebholz , Philipp W. Schroeder

We introduce a family of discontinuous Galerkin methods to approximate the eigenvalues and eigenfunctions of a Stokes-Brinkman type of problem based in the interior penalty strategy. Under the standard assumptions on the meshes and a…

Numerical Analysis · Mathematics 2025-07-17 Felipe Lepe , Gonzalo Rivera , Jesus Vellojin

This work focuses on the development of efficient solvers for the pseudo-stress formulation of the unsteady Stokes problem, discretised by means of a discontinuous Galerkin method on polytopal grids (PolyDG). The introduction of the…

Numerical Analysis · Mathematics 2026-02-04 Paola F. Antonietti , Alessandra Cancrini , Gabriele Ciaramella

This paper presents a pressure-robust discretizations, specifically within the context of optimal control problems for the Stokes-Darcy system. The study meticulously revisits the formulation of the divergence constraint and the enforcement…

Numerical Analysis · Mathematics 2025-02-25 Jingshi Li , Jiachuan Zhang , Ran Zhang

In this paper we propose a novel arbitrary high order accurate semi-implicit space-time DG method for the solution of the three-dimensional incompressible Navier-Stokes equations on staggered unstructured curved tetrahedral meshes. As…

Numerical Analysis · Mathematics 2016-06-22 Maurizio Tavelli , Michael Dumbser

In order to perform electroencephalography (EEG) source reconstruction, i.e., to localize the sources underlying a measured EEG, the electric potential distribution at the electrodes generated by a dipolar current source in the brain has to…

Computational Engineering, Finance, and Science · Computer Science 2016-11-16 Christian Engwer , Johannes Vorwerk , Jakob Ludewig , Carsten H. Wolters

We present a high-order hybridized discontinuous Galerkin (HDG) method for the fully coupled time-dependent Stokes-Darcy-transport problem where the fluid viscosity and source/sink terms depend on the concentration and the…

Numerical Analysis · Mathematics 2023-07-07 Aycil Cesmelioglu , Dinh Dong Pham , Sander Rhebergen

In this paper, for the Stokes eigenvalue problem in $d$-dimensional case $(d=2,3)$, we present an a posteriori error estimate of residual type of the mixed discontinuous Galerkin finite element method using $P_{k}-P_{k-1}$ element $(k\geq…

Numerical Analysis · Mathematics 2022-09-14 L. L. Sun , H. Bi , Y. D. Yang

Pointwise divergence free velocity field approximations of the Stokes system are gaining popularity due to their necessity in precise modelling of physical flow phenomena. Several methods have been designed to satisfy this requirement;…

Numerical Analysis · Mathematics 2023-09-15 Nathan Sime , Paul Houston , Cian R. Wilson , Peter E. van Keken

We introduce a hybridized discontinuous Galerkin method for the incompressible Reynolds Averaged Navier-Stokes equations coupled with the Spalart-Allmaras one equation turbulence model. With a special choice of velocity and pressure spaces…

Numerical Analysis · Mathematics 2024-12-20 Eric L. Peters , John A. Evans