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In this paper, a space-time discontinuous Galerkin finite element method for distributed optimal control problems governed by unsteady diffusion-convection-reaction equations with control constraints is studied. Time discretization is…

Optimization and Control · Mathematics 2013-08-09 Tuğba Akman , Bülent Karasözen

We study the numerical approximation by space-time finite element methods of a multi-physics system coupling hyperbolic elastodynamics with parabolic transport and modeling poro- and thermoelasticity. The equations are rewritten as a…

Numerical Analysis · Mathematics 2023-02-14 Markus Bause , Mathias Anselmann , Uwe Köcher , Florin A. Radu

We propose a new discrete element method supporting general polyhedral meshes. The method can be understood as a lowest-order discontinuous Galerkin method parametrized by the continuous mechanical parameters (Young's modulus and Poisson's…

Numerical Analysis · Mathematics 2022-02-18 Frédéric Marazzato , Alexandre Ern , Laurent Monasse

In this paper we propose and analyze a Discontinuous Galerkin method for a linear parabolic problem with dynamic boundary conditions. We present the formulation and prove stability and optimal a priori error estimates for the fully discrete…

Numerical Analysis · Mathematics 2015-01-21 Paola F. Antonietti , Maurizio Grasselli , Simone Stangalino , Marco Verani

We present an embedded-hybridizable discontinuous Galerkin finite element method for the total pressure formulation of the quasi-static poroelasticity model. Although the displacement and the Darcy velocity are approximated by discontinuous…

Numerical Analysis · Mathematics 2022-07-27 Aycil Cesmelioglu , Jeonghun J. Lee , Sander Rhebergen

We present and analyze a discontinuous Galerkin method for the numerical modeling of the non-linear fully-coupled thermo-hydro-mechanic problem. We propose a high-order symmetric weighted interior penalty scheme that supports general…

Numerical Analysis · Mathematics 2023-11-28 Stefano Bonetti , Michele Botti , Paola F. Antonietti

We consider semi-discrete discontinuous Galerkin approximations of a general elastodynamics problem, in both {\it displacement} and {\it displacement-stress} formulations. We present the stability analysis of all the methods in the natural…

Numerical Analysis · Mathematics 2013-10-31 Paola F. Antonietti , Blanca Ayuso de Dios , Ilario Mazzieri , Alfio Quarteroni

The aim of this work is to introduce and analyze a finite element discontinuous Galerkin method on polygonal meshes for the numerical discretization of acoustic waves propagation through poroelastic materials. Wave propagation is modeled by…

Numerical Analysis · Mathematics 2021-04-14 Paola F. Antonietti , Michele Botti , Ilario Mazzieri , Simone Nati Poltri

In this work, we present a new high order Discontinuous Galerkin time integration scheme for second-order (in time) differential systems that typically arise from the space discretization of the elastodynamics equation. By rewriting the…

Numerical Analysis · Mathematics 2021-12-06 Paola F. Antonietti , Ilario Mazzieri , Francesco Migliorini

In this paper, we study the stabilizer-free weak Galerkin methods on polytopal meshes for a class of second order elliptic boundary value problems of divergence form and with gradient nonlinearity in the principal coefficient. With certain…

Numerical Analysis · Mathematics 2020-02-04 Xiu Ye , Shangyou Zhang , Yunrong Zhu

We consider the initial/boundary value problem for a diffusion equation involving multiple time-fractional derivatives on a bounded convex polyhedral domain. We analyze a space semidiscrete scheme based on the standard Galerkin finite…

Numerical Analysis · Mathematics 2015-06-18 Bangti Jin , Raytcho Lazarov , Yikan Liu , Zhi Zhou

We study preconditioning techniques for discontinuous Galerkin discretizations of isotropic linear elasticity problems in primal (displacement) formulation. We propose subspace correction methods based on a splitting of the vector valued…

Numerical Analysis · Mathematics 2011-11-01 Blanca Ayuso de Dios , Ivan Georgiev , Johannes Kraus , Ludmil Zikatanov

This work aims to construct and analyze a discontinuous Galerkin method on polytopal grids (PolydG) to solve the pseudo-stress formulation of the unsteady Stokes problem. The pseudo-stress variable is introduced due to the growing interest…

Numerical Analysis · Mathematics 2025-12-03 Paola F. Antonietti , Michele Botti , Alessandra Cancrini , Ilario Mazzieri

In this paper we propose a new finite element discretization for the two-field formulation of poroelasticity which uses the elastic displacement and the pore pressure as primary variables. The main goal is to develop a numerical method with…

Numerical Analysis · Mathematics 2023-08-08 Jeonghun J. Lee , Jacob Moore

This work studies discontinuous Galerkin (DG) approximations of the boundary value problem for homogeneous transversely isotropic linear elastic bodies. Low-order approximations on triangles are adopted, with the use of three interior…

Analysis of PDEs · Mathematics 2019-11-26 B. J. Grieshaber , F. Rasolofoson , B. D. Reddy

We develop a hybrid spatial discretization for the wave equation in second order form, based on high-order accurate finite difference methods and discontinuous Galerkin methods. The hybridization combines computational efficiency of finite…

Numerical Analysis · Mathematics 2022-10-26 Siyang Wang , Gunilla Kreiss

We develop and analyze a class of structure-preserving discontinuous Galerkin schemes for the nonlinear Vlasov-Poisson-Fokker-Planck model, reformulated as a hyperbolic system through a Hermite expansion in the velocity variable. We…

Numerical Analysis · Mathematics 2026-03-30 Yi Cai , Alain Blaustein , Tao Xiong , Francis Filbet

One- and multi-dimensional stochastic Maxwell equations with additive noise are considered in this paper. It is known that such system can be written in the multi-symplectic structure, and the stochastic energy increases linearly in time.…

Numerical Analysis · Mathematics 2022-05-04 Jiawei Sun , Chi-Wang Shu , Yulong Xing

We present a method for linear stability analysis of systems with parametric uncertainty formulated in the stochastic Galerkin framework. Specifically, we assume that for a model partial differential equation, the parameter is given in the…

Numerical Analysis · Mathematics 2026-01-14 Bedřich Sousedík , Kookjin Lee

We study linear parabolic initial-value problems in a space-time variational formulation based on fractional calculus. This formulation uses "time derivatives of order one half" on the bi-infinite time axis. We show that for linear,…

Numerical Analysis · Mathematics 2015-01-20 Stig Larsson , Christoph Schwab