Related papers: Reduced Basis A Posteriori Error Bounds for the In…
Parametric model order reduction using reduced basis methods can be an effective tool for obtaining quickly solvable reduced order models of parametrized partial differential equation problems. With speedups that can reach several orders of…
We consider fully discrete embedded finite element approximations for a shallow water hyperbolic problem and its reduced-order model. Our approach is based on a fixed background mesh and an embedded reduced basis. The Shifted Boundary…
We present an abstract framework for a posteriori error estimation for approximations of scalar parabolic evolution equations, based on elliptic reconstruction techniques [10, 9, 3, 5]. In addition to its original application (to derive…
We derive globally reliable a posteriori error estimators for a PDE-constrained optimization problem involving linear models in fluid dynamics as state equation; control constraints are also considered. The corresponding local error…
We consider finite element solutions to optimization problems, where the state depends on the possibly constrained control through a linear partial differential equation. Basing upon a reduced and rescaled optimality system, we derive a…
This article proposes modifications to standard low order finite element approximations of the Stokes system with the goal of improving both the approximation quality and the parallel algebraic solution process. Different from standard…
The Stokes-Brinkman equations model fluid flow in highly heterogeneous porous media. In this paper, we consider the numerical solution of the Stokes-Brinkman equations with stochastic permeabilities, where the permeabilities in subdomains…
This paper develops and discusses a residual-based a posteriori error estimator for parabolic surface partial differential equations on closed stationary surfaces. The full discretization uses the surface finite element method in space and…
Lower a posteriori error bounds obtained using the standard bubble function approach are reviewed in the context of anisotropic meshes. A numerical example is given that clearly demonstrates that the short-edge jump residual terms in such…
The numerical approximation of convection-dominated problems continues to remain subject of strong interest. Families of stabilization techniques for finite element methods were developed in the past. Adaptive techniques based on a…
For a family of stabilized mixed finite element methods for the Stokes equations a complete a priori and a posteriori error analysis is given.
In this paper we present a reduced basis method which yields structure-preservation and a tight a posteriori error bound for the simulation of the damped wave equations on networks. The error bound is based on the exponential decay of the…
Recently, the Shifted Boundary Method (SBM) was proposed within the class of unfitted (or immersed, or embedded) finite element methods. By reformulating the original boundary value problem over a surrogate (approximate) computational…
In this paper we develop an a posteriori error analysis for the stationary Stokes-Darcy coupled problem approximated by conforming finite element method on isotropic meshes in $\mathbb{R}^d$, $d\in\{2,3\}$. The approach utilizes a new…
In two dimensions, we propose and analyze an a posteriori error estimator for finite element approximations of the stationary Navier Stokes equations with singular sources on Lipschitz, but not necessarily convex, polygonal domains. Under a…
A posteriori error estimators for the symmetric mixed finite element methods for linear elasticity problems of Dirichlet and mixed boundary conditions are proposed. Stability and efficiency of the estimators are proved. Finally, we provide…
Motivated by problems in contact mechanics, we propose a duality approach for computing approximations and associated a posteriori error bounds to solutions of variational inequalities of the first kind. The proposed approach improves upon…
The paper is concerned with a posteriori error bounds for a wide class of numerical schemes, for $n\times n$ hyperbolic conservation laws in one space dimension. These estimates are achieved by a "post-processing algorithm", checking that…
We present a reduced basis technique for long-time integration of parametrized incompressible turbulent flows. The new contributions are threefold. First, we propose a constrained Galerkin formulation that corrects the standard Galerkin…
Time-fractional parabolic equations with a Caputo time derivative are considered. For such equations, we explore and further develop the new methodology of the a-posteriori error estimation and adaptive time stepping proposed in [7]. We…