A Local Discontinuous Galerkin Approximation for the p-Navier–Stokes System, Part I: Convergence Analysis

A Kaltenbach, M RůžIčka - SIAM Journal on Numerical Analysis, 2023 - SIAM
In the present paper, we propose a local discontinuous Galerkin approximation for fully
nonhomogeneous systems of-Navier–Stokes type. On the basis of the primal formulation, we …

Convergence analysis of a local discontinuous Galerkin approximation for nonlinear systems with balanced Orlicz-structure

A Kaltenbach, M Růžička - ESAIM: Mathematical Modelling and …, 2023 - esaim-m2an.org
In this paper, we investigate a Local Discontinuous Galerkin (LDG) approximation for
systems with balanced Orlicz-structure. We propose a new numerical flux, which yields …

Error analysis for a Crouzeix–Raviart approximation of the p-Dirichlet problem

A Kaltenbach - Journal of Numerical Mathematics, 2024 - degruyter.com
In the present paper, we examine a Crouzeix–Raviart approximation for non-linear partial
differential equations having a (p, δ)-structure for some p∈(1,∞) and δ⩾ 0. We establish a …

A Local Discontinuous Galerkin Approximation for the -Navier–Stokes System, Part II: Convergence Rates for the Velocity

A Kaltenbach, M Růžička - SIAM Journal on Numerical Analysis, 2023 - SIAM
In the present paper, we prove convergence rates for the velocity of the local discontinuous
Galerkin approximation, proposed in Part I of the paper [A. Kaltenbach and M. Růžička …

A Hybridizable Discontinuous Galerkin Method for the -Laplacian

B Cockburn, J Shen - SIAM Journal on Scientific Computing, 2016 - SIAM
We propose the first hybridizable discontinuous Galerkin method for the p-Laplacian
equation. When using polynomials of degree k≧0 for the approximation spaces of u, ∇u …

Error analysis for a Crouzeix–Raviart approximation of the variable exponent Dirichlet problem

AK Balci, A Kaltenbach - IMA Journal of Numerical Analysis, 2024 - academic.oup.com
In the present paper, we examine a Crouzeix–Raviart approximation of the-Dirichlet
problem. We derive a medius error estimate, ie, a best-approximation result, which holds for …

A Local Discontinuous Galerkin Approximation for the -Navier–Stokes System, Part III: Convergence Rates for the Pressure

A Kaltenbach, M Růžička - SIAM Journal on Numerical Analysis, 2023 - SIAM
In the present paper, we prove convergence rates for the pressure of the local discontinuous
Galerkin approximation, proposed in Part I of the paper [A. Kaltenbach and M. Růžička …

Finite element discretization of the steady, generalized Navier–Stokes equations with inhomogeneous Dirichlet boundary conditions

J Jeßberger, A Kaltenbach - SIAM Journal on Numerical Analysis, 2024 - SIAM
We propose a finite element discretization for the steady, generalized Navier–Stokes
equations for fluids with shear-dependent viscosity, completed with inhomogeneous …

Analysis of a fully-discrete, non-conforming approximation of evolution equations and applications

A Kaltenbach, M Růžička - … Models and Methods in Applied Sciences, 2023 - World Scientific
In this paper, we consider a fully-discrete approximation of an abstract evolution equation
deploying a non-conforming spatial approximation and finite differences in time (Rothe …

A C0 Interior Penalty Discontinuous Galerkin Method and an equilibrated a posteriori error estimator for a nonlinear fourth order elliptic boundary value problem of p …

RHW Hoppe - ESAIM: Mathematical Modelling and Numerical …, 2022 - esaim-m2an.org
We consider a C 0 Interior Penalty Discontinuous Galerkin (C0IPDG) approximation of a
nonlinear fourth order elliptic boundary value problem of p-biharmonic type and an …