相关论文: Flexible goal-oriented adaptivity for higher-order…
Advective trapping occurs when solute enters low velocity zones in heterogeneous porous media. Classical local modeling approaches combine the impact of slow advection and diffusion into a hydrodynamic dispersion coefficient and many…
A finite element solution coupled with an interior penalty discontinuous Galerkin solution are defined for the approximation of the coupled 3D-1D solute transport problem. Under sufficient regularity for the weak solutions, optimal error…
A $p$-adaptive discontinuous Galerkin time-domain method is developed to obtain high-order solutions to electromagnetic scattering problems. A novel feature of the proposed method is the use of divergence error to drive the $p$-adaptive…
In this paper we present distributed and adaptive algorithms for motion coordination of a group of m autonomous vehicles. The vehicles operate in a convex environment with bounded velocity and must service demands whose time of arrival,…
We present a new method for approximating solutions to the incompressible miscible displacement problem in porous media. At the discrete level, the coupled nonlinear system has been split into two linear systems that are solved…
The heart of the a priori and a posteriori error control in convex minimization problems is the sharp control of the differences of discrete and exact minimal energy. Conforming finite element discretizations for p-Laplace type minimization…
Numerical simulations of flow and transport in porous media usually rely on hybrid-dimensional models, i.e., the fracture is considered as objects of a lower dimension compared to the embedding matrix. Such models are usually combined with…
In this article we develop a convergence theory for goal-oriented adaptive finite element algorithms designed for a class of second-order semilinear elliptic equations. We briefly discuss the target problem class, and introduce several…
An adaptive discretization refinement strategy for steady state discrete mesoscale models of coupled mechanics and mass transport in concrete is presented. Coupling is provided by two phenomena: the Biot's theory of poromechanics and an…
We study the contribution of advection by thermal velocity fluctuations to the effective diffusion coefficient in a mixture of two identical fluids. The steady-state diffusive flux in a finite system subject to a concentration gradient is…
We develop a reduced-order framework for optimizing mixing in two-dimensional incompressible flows. Instead of optimizing the full transport PDE, the method maximizes the length of advected material interfaces, leading to a…
This paper introduces a novel framework for model adaptivity in the context of heterogeneous multiscale problems. The framework is based on the idea to interpret model adaptivity as a minimization problem of local error indicators, that are…
We present a numerical analysis of a higher order unfitted space-time Finite Element method applied to a convection-diffusion model problem posed on a moving bulk domain. The method uses isoparametric space-time mappings for the geometry…
This work is aimed at the derivation of reliable and efficient a posteriori error estimates for convection-dominated diffusion problems motivated by a linear Fokker-Planck problem appearing in computational neuroscience. We obtain…
In this paper we propose a new finite element discretization for the two-field formulation of poroelasticity which uses the elastic displacement and the pore pressure as primary variables. The main goal is to develop a numerical method with…
The potential of the hybridized discontinuous Galerkin (HDG) method has been recognized for the computation of stationary flows. Extending the method to time-dependent problems can, e.g., be done by backward difference formulae (BDF) or…
This work recasts time-dependent optimal control problems governed by partial differential equations in a Dynamic Mode Decomposition with control framework. Indeed, since the numerical solution of such problems requires a lot of…
This paper is concerned with the numerical solution of porous-media flow and transport problems , i. e. heterogeneous, advection-diffusion problems. Its aim is to investigate numerical schemes for these problems in which different time…
In this paper we formulate and analyse adaptive (space-time) least-squares finite element methods for the solution of convection-diffusion equations. The convective derivative $\mathbf{v} \cdot \nabla u$ is considered as part of the total…
We present a new implicit higher-order finite element (FE) approach to efficiently model compressible multicomponent fluid flow on unstructured grids and in fractured porous subsurface formations. The scheme is sequential implicit:…