Related papers: Optimal error estimate for a space-time discretiza…
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…
In this article we obtain an optimal best approximation type result for fully discrete approximations of the transient Stokes problem. For the time discretization we use the discontinuous Galerkin method and for the spatial discretization…
The paper presents error estimates within a unified abstract framework for the analysis of FEM for boundary value problems with linear diffusion-convection-reaction equations and boundary conditions of mixed type. Since neither conformity…
In this paper, we employ a space-time finite element method to discretize the parabolic initial-boundary value problem and extend its error analysis with refined estimates on unstructured space-time meshes. We establish higher-order…
Implicit constitutive theory provides a very general framework for fluid flow models, including both Newtonian and generalized Newtonian fluids, where the Cauchy stress tensor and the rate of strain tensor are assumed to be related by an…
We show error estimates for a cut finite element approximation of a second order elliptic problem with mixed boundary conditions. The error estimates are of low regularity type where we consider the case when the exact solution $u \in H^s$…
We consider fully discrete numerical schemes for a downscaling data assimilation algorithm aimed at approximating the velocity field of the 2D Navier-Stokes equations corresponding to given coarse mesh observational measurements. The time…
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…
This paper is concerned with minimization of a fourth-order linearized Canham-Helfrich energy subject to Dirichlet boundary conditions on curves inside the domain. Such problems arise in the modeling of the mechanical interaction of…
In this paper we present a new Eulerian finite element method for the discretization of scalar partial differential equations on evolving surfaces. In this method we use the restriction of standard space-time finite element spaces on a…
This paper presents a geometric variational discretization of compressible fluid dynamics. The numerical scheme is obtained by discretizing, in a structure preserving way, the Lie group formulation of fluid dynamics on diffeomorphism groups…
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…
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…
We propose a new class of finite element approximations to ideal compressible magnetohydrodynamic equations in smooth regime. Following variational approximations developed for fluid models in the last decade, our discretizations are built…
We consider the Shallow Water equations in the supercritical and subcritical cases in one space variable,posed in a finite spatial interval with characteristic boundary conditions at the endpoints, which, as is well known, are…
A proof of convergence is given for bulk--surface finite element semi-discretisation of the Cahn--Hilliard equation with Cahn--Hilliard-type dynamic boundary conditions in a smooth domain. The semi-discretisation is studied in the weak…
In this paper we investigate an adaptive discretization strategy for ill-posed linear prob- lems combined with a regularization from a class of semiiterative methods. We show that such a discretization approach in combination with a…
In this paper we consider the semi-discretization in space of a first order scalar transport equation. For the space discretization we use standard continuous finite elements. To obtain stability we add a penalty on the jump of the gradient…
In this paper, both semidiscrete and fully discrete finite element methods are analyzed for the penalized two-dimensional unsteady Navier-Stokes equations with nonsmooth initial data. First order backward Euler method is applied for the…
This paper is devoted to the error analysis of a time-spectral algorithm for fractional diffusion problems of order $\alpha$ ($0 < \alpha < 1$). The solution regularity in the Sobolev space is revisited, and new regularity results in the…