English
Related papers

Related papers: Error Estimates For A Linear Folding Model

200 papers

We present a new residual-type energy-norm a posteriori error analysis for interior penalty discontinuous Galerkin (dG) methods for linear elliptic problems. The new error bounds are also applicable to dG methods on meshes consisting of…

Numerical Analysis · Mathematics 2023-07-13 Andrea Cangiani , Zhaonan Dong , Emmanuil H. Georgoulis

We provide a posteriori error estimates for a discontinuous Galerkin scheme for the parabolic-elliptic Keller-Segel system in 2 or 3 space dimensions. The estimates are conditional, in the sense that an a posteriori computable quantity…

Numerical Analysis · Mathematics 2024-06-12 Jan Giesselmann , Kiwoong Kwon

In recent years, high-order finite element methods on high-order meshes have attracted considerable attention. This work investigates the isoparametric upwind discontinuous Galerkin method for the radiation transport equation on a bounded…

Numerical Analysis · Mathematics 2026-05-06 Changhui Yao , Yunpan Ma , Lingxiao Li

In the present study, an interior-exterior penalty discontinuous Galerkin finite element method (DG-FEM) is analysed for solving Elastohydrodynamic lubrication (EHL) line and point contact problems. The existence of discrete penalized…

Numerical Analysis · Mathematics 2022-07-08 Peeyush Singh

In this paper we establish a best approximation property of fully discrete Galerkin finite element solutions of second order parabolic problems on convex polygonal and polyhedral domains in the $L^\infty$ norm. The discretization method…

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

In this paper we investigate a priori error estimates for the space-time Galerkin finite element discretization of a simplified semilinear gradient enhanced damage model. The model equations are of a special structure as the state equation…

Optimization and Control · Mathematics 2020-04-14 Marita Holtmannspötter , Arnd Rösch

This paper is concerned with goal-oriented a posteriori error estimation for nonlinear functionals in the context of nonlinear variational problems solved with continuous Galerkin finite element discretizations. A two-level, or discrete,…

Computational Engineering, Finance, and Science · Computer Science 2025-01-10 Brian N. Granzow , D. Thomas Seidl , Stephen D. Bond

In this paper we investigate a priori error estimates for the space-time Galerkin finite element discretization of an optimal control problem governed by a simplified linear gradient enhanced damage model. The model equations are of a…

Numerical Analysis · Mathematics 2020-04-10 Marita Holtmannspötter , Arnd Rösch , Boris Vexler

In this paper we establish best approximation property of fully discrete Galerkin solutions of second order parabolic problems on convex polygonal and polyhedral domains in the $L^\infty(I;W^{1,\infty}(\Om))$ norm. The discretization method…

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

In this paper, we derive improved a priori error estimates for families of hybridizable interior penalty discontinuous Galerkin (H-IP) methods using a variable penalty for second-order elliptic problems. The strategy is to use a…

Numerical Analysis · Mathematics 2021-10-06 Gregory Etangsale , Marwan Fahs , Vincent Fontaine , Nalitiana Rajaonison

This paper is concerned with developing accurate and efficient numerical methods for one-dimensional fully nonlinear second order elliptic and parabolic partial differential equations (PDEs). In the paper we present a general framework for…

Numerical Analysis · Mathematics 2012-12-04 Xiaobing Feng , Thomas Lewis

The maximal regularity property of discontinuous Galerkin methods for linear parabolic equations is used together with variational techniques to establish a priori and a posteriori error estimates of optimal order under optimal regularity…

Numerical Analysis · Mathematics 2024-12-13 Georgios Akrivis , Stig Larsson

We derive a posteriori error bounds for a quasilinear parabolic problem, which is approximated by the $hp$-version interior penalty discontinuous Galerkin method (IPDG). The error is measured in the energy norm. The theory is developed for…

Numerical Analysis · Mathematics 2013-09-20 Emmanuil H. Georgoulis , Omar Lakkis

Isogeometric Analysis is a spline-based discretization method to partial differential equations which shows the approximation power of a high-order method. The number of degrees of freedom, however, is as small as the number of degrees of…

Numerical Analysis · Mathematics 2021-04-22 Stefan Takacs

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

We present and analyze a discontinuous Galerkin method for the numerical modeling of a Kelvin-Voigt thermo/poro-viscoelastic problem. We present the derivation of the model and we develop a stability analysis in the continuous setting that…

Numerical Analysis · Mathematics 2025-08-01 Stefano Bonetti , Mattia Corti

We propose an efficient variant of a primal Discontinuous Galerkin method with interior penalty for the second order elliptic equations on very general meshes (polytopes with eventually curved boundaries). Efficiency, especially when higher…

Numerical Analysis · Mathematics 2019-03-18 Alexei Lozinski

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

This paper studies the family of interior penalty discontinuous Galerkin methods for solving the Herrmann formulation of the linear elasticity eigenvalue problem in heterogeneous media. By employing a weighted Lam\'e coefficient norm within…

Numerical Analysis · Mathematics 2024-02-28 Arbaz Khan , Felipe Lepe , Jesus Vellojin

In this paper, we are concerned with a nonlinear optimal control problem of ordinary differential equations. We consider a discretization of the problem with the discontinuous Galerkin method with arbitrary order $r \in \mathbb{N}\cup…

Numerical Analysis · Mathematics 2020-05-25 Woocheol Choi , Young-Pil Choi