Related papers: Multi-Adaptive Galerkin Methods for ODEs I
This paper presents high order accurate discontinuous Galerkin (DG) methods for wave problems on moving curved meshes with general choices of basis and quadrature. The proposed method adopts an arbitrary Lagrangian-Eulerian (ALE)…
In this work, the authors introduce a generalized weak Galerkin (gWG) finite element method for the time-dependent Oseen equation. The generalized weak Galerkin method is based on a new framework for approximating the gradient operator.…
We derive and discuss a posteriori error estimators for Galerkin and collocation IGA boundary element methods for weakly-singular integral equations of the first-kind in 2D. While recent own work considered the Faermann residual error…
We propose a robust, adaptive coarse-grid correction scheme for matrix-free geometric multigrid targeting PDEs with strongly varying coefficients. The method combines uniform geometric coarsening of the underlying grid with heterogeneous…
We establish rigorous \emph{a posteriori} error bounds for a space-time finite element method of arbitrary order discretising linear wave problems in second order formulation. The method combines standard finite elements in space and…
In this paper we continue our work on adaptive timestep control for weakly non- stationary problems. The core of the method is a space-time splitting of adjoint error representations for target functionals due to S\"uli and Hartmann. The…
This article presents a unified mathematical framework for modeling coupled poro-viscoelastic and thermo-viscoelastic phenomena, formulated as a system of first-order in time partial differential equations. The model describes the evolution…
Motivated by considering partial differential equations arising from conservation laws posed on evolving surfaces, a new numerical method for an advection problem is developed and simple numerical tests are performed. The method is based on…
In this paper we study the behavior of finite dimensional fixed point iterations, induced by discretization of a continuous fixed point iteration defined within a Banach space setting. We show that the difference between the discrete…
The paper focuses on unconditionally optimal error analysis of the fully discrete Galerkin finite element methods for a general nonlinear parabolic system in $\R^d$ with $d=2,3$. In terms of a corresponding time-discrete system of PDEs as…
We consider evolutionary systems, i.e. systems of linear partial differential equations arising from the mathematical physics. For these systems there exists a general solution theory in exponentially weighted spaces which can be exploited…
In this paper, we present two Hermite polynomial based approaches to derive one-step numerical integrators for mechanical systems. These methods are based on discretizing the configuration using Hermite polynomials which leads to numerical…
In this work we construct reliable a posteriori estimates for some discontinuous Galerkin schemes applied to nonlinear systems of hyperbolic conservation laws. We make use of appropriate reconstructions of the discrete solution together…
In this work we recast parametrized time dependent optimal control problems governed by partial differential equations in a saddle point formulation and we propose reduced order methods as an effective strategy to solve them. Indeed, on one…
The problem of designing adaptive stepsize sequences for the gradient descent method applied to convex and locally smooth functions is studied. We take an adaptive control perspective and design update rules for the stepsize that make use…
Critical points of energy functionals, which are of broad interest, for instance, in physics and chemistry, in solid and quantum mechanics, in material science, or in general diffusion-reaction models arise as solutions to the associated…
We present a nonlinear stabilized Lagrange-Galerkin scheme for the Oseen-type Peterlin viscoelastic model. Our scheme is a combination of the method of characteristics and Brezzi-Pitk\"aranta's stabilization method for the conforming linear…
The numerical solution of time-dependent radiative transfer problems is challenging, both, due to the high dimension as well as the anisotropic structure of the underlying integro-partial differential equation. In this paper we propose a…
We propose a projection-based model order reduction method for the solution of parameter-dependent dynamical systems. The proposed method relies on the construction of time-dependent reduced spaces generated from evaluations of the solution…
This paper introduces a novel a posteriori error estimation framework for the enriched Galerkin (EG) finite element method applied to linear parabolic equations. While the EG method has been recognized for its local conservation property…