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This paper is devoted to the numerical analysis of a control constrained distributed optimal control problem subject to a time fractional diffusion equation with non-smooth initial data. The solutions of state and co-state are decomposed…

Numerical Analysis · Mathematics 2020-10-06 Tao Wang , Binjie Li , Xiaoping Xie

In this paper, we develop an arbitrary-order locking-free enriched Galerkin method for the linear elasticity problem using the stress-displacement formulation in both two and three dimensions. The method is based on the mixed discontinuous…

Numerical Analysis · Mathematics 2023-11-13 Zhongshu Zhao , Hui Peng , Qilong Zhai , Qian Zhang

A new discontinuous Galerkin finite element method for the Stokes equations is developed in the primary velocity-pressure formulation. This method employs discontinuous polynomials for both velocity and pressure on general…

Numerical Analysis · Mathematics 2021-05-05 Xiu Ye , Shangyou Zhang

The main goal of the paper is to establish time semidiscrete and space-time fully discrete maximal parabolic regularity for the time discontinuous Galerkin solution of linear parabolic equations. Such estimates have many applications. They…

Numerical Analysis · Mathematics 2018-08-20 Dmitriy Leykekhman , Boris Vexler

We present a high order time-domain nodal discontinuous Galerkin method for wave problems on hybrid meshes consisting of both wedge and tetrahedral elements. We allow for vertically mapped wedges which can be deformed along the extruded…

Numerical Analysis · Mathematics 2016-11-02 Jesse Chan , Zheng Wang , Russell J. Hewett , T. Warburton

We study discontinuous Galerkin approximations of the $p$--biharmonic equation from a variational perspective. We propose a discrete variational formulation of the problem based on a appropriate definition of a finite element Hessian and…

Numerical Analysis · Mathematics 2015-09-23 Tristan Pryer

This paper is devoted to a weak Galerkin (WG) finite element method for linear poroelasticity problems where weakly defined divergence and gradient operators over discontinuous functions are introduced. We establish both the continuous and…

Numerical Analysis · Mathematics 2022-08-10 Shanshan Gu , Shimin Chai , Chenguang Zhou

In this paper, a time-domain discontinuous Galerkin (TDdG) finite element method for the full system of Maxwell's equations in optics and photonics is investigated, including a complete proof of a semi-discrete error estimate. The new…

Numerical Analysis · Mathematics 2026-02-04 Asad Anees , Lutz Angermann

We derive well-posed boundary conditions for the linearized Serre equations in one spatial dimension by utilizing the energy method. An energy stable and conservative discontinuous Galerkin spectral element method with simple upwind…

Numerical Analysis · Mathematics 2023-04-26 Kenny Wiratama , Kenneth Duru , Stephen Roberts , Christopher Zoppou

In this work, we propose and investigate stable high-order collocation-type discretisations of the discontinuous Galerkin method on equidistant and scattered collocation points. We do so by incorporating the concept of discrete least…

Numerical Analysis · Mathematics 2021-02-24 Jan Glaubitz , Philipp Oeffner

We present and analyze a high-order discontinuous Galerkin method for the space discretization of the wave propagation model in thermo-poroelastic media. The proposed scheme supports general polytopal grids. Stability analysis and…

Numerical Analysis · Mathematics 2023-06-28 Stefano Bonetti , Michele Botti , Ilario Mazzieri , Paola F. Antonietti

This work examines the distributed optimal control of generalized Oseen equations with non-constant viscosity. We propose and analyze a new conforming augmented mixed finite element method and a Discontinuous Galerkin (DG) method for the…

Numerical Analysis · Mathematics 2025-08-18 Harpal Singh , Arbaz Khan

An hyperelastic biphasic model is presented. For slow-draining problems (permeability less than 1\times10-2 mm4 N-1 s-1), numerical instabilities in the form of non-physical oscillations in the pressure field are observed in 3D problems…

Numerical Analysis · Mathematics 2011-11-01 Julien Vignollet , Chris J. Pearce , Lukasz Kaczmarczyk

In this paper we propose a novel arbitrary high order accurate semi-implicit space-time discontinuous Galerkin method for the solution of the two dimensional incompressible Navier-Stokes equations on staggered unstructured triangular…

Numerical Analysis · Mathematics 2014-12-04 Maurizio Tavelli , Michael Dumbser

We prove error estimates for a finite element approximation of viscoelastic dynamics based on continuous Galerkin in space and time, both in energy norm and in $L^2$ norm. The proof is based on an error representation formula using a…

Numerical Analysis · Mathematics 2024-03-26 Martin Björklund , Karl Larsson , Mats G. Larson

This paper is concerned with the approximation of linear and nonlinearinitial-boundary-value problems of pseudo-parabolic equations with Dirichlet boundary conditions. They are discretized in space by spectral Galerkin and collocation…

Numerical Analysis · Mathematics 2020-02-26 Eduardo Abreu , Angel Durán

This paper proposes and analyzes a class of new weak Galerkin (WG) finite element methods for 2- and 3-dimensional linear elasticity problems. The methods use discontinuous piecewise-polynomial approximations of degrees $k(\geq 0)$ for the…

Numerical Analysis · Mathematics 2017-10-24 Gang Chen , Xiaoping Xie

In the context of Discontinuous Galerkin methods, we study approximations of nonlinear variational problems associated with convex energies. We propose element-wise nonconforming finite element methods to discretize the continuous…

Numerical Analysis · Mathematics 2025-02-05 Georgios Grekas , Konstantinos Koumatos , Charalambos Makridakis , Andreas Vikelis

We consider a semilinear parabolic equation with a large class of nonlinearities without any growth conditions. We discretize the problem with a discontinuous Galerkin scheme dG(0) in time (which is a variant of the implicit Euler scheme)…

Numerical Analysis · Mathematics 2018-08-17 Dominik Meidner , Boris Vexler

In this article we study the numerical approximation of incompressible miscible displacement problems with a linearised Crank-Nicolson time discretisation, combined with a mixed finite element and discontinuous Galerkin method. At the heart…

Numerical Analysis · Mathematics 2011-11-28 Max Jensen , Ruediger Mueller