Related papers: Online adaptive algorithm for Constraint Energy Mi…
In this research, an online basis enrichment strategy for the constraint energy minimizing generalized multiscale finite element method in mixed formulation is proposed. The online approach is based on the technique of oversampling. One…
Offline computation is an essential component in most multiscale model reduction techniques. However, there are multiscale problems in which offline procedure is insufficient to give accurate representations of solutions, due to the fact…
In this work, we develop an online adaptive enrichment method within the framework of the Constraint Energy Minimizing Generalized Multiscale Finite Element Method (CEM-GMsFEM) for solving the linear heterogeneous poroelasticity models with…
In this paper, we develop an adaptive Generalized Multiscale Discontinuous Galerkin Method (GMs-DGM) for a class of high-contrast flow problems, and derive a-priori and a-posteriori error estimates for the method. Based on the a-posteriori…
In this paper, we consider the offline and online Constraint Energy Minimizing Generalized Mul- tiscale Finite Element Method (CEM-GMsFEM) for high-contrast linear elasticity problem. Offline basis construction starts with an auxiliary…
In this research, we develop an online enrichment framework for goal-oriented adaptivity within the generalized multiscale finite element method for flow problems in heterogeneous media. The method for approximating the quantity of interest…
Local multiscale methods often construct multiscale basis functions in the offline stage without taking into account input parameters, such as source terms, boundary conditions, and so on. These basis functions are then used in the online…
In this paper, we propose offline and online adaptive enrichment algorithms for the generalized multiscale approximation of a mixed finite element method with velocity elimination to solve the subsurface flow problem in high-contrast and…
A framework for performing dynamic mesh adaptation with the discontinuous Galerkin method (DGM) is presented. Adaptations include modifications of the local mesh step size (h-adaptation) and the local degree of the approximating polynomials…
In this paper, we consider the constrained energy minimizing generalized multiscale finite element method (CEM-GMsFEM) with discontinuous Galerkin (DG) coupling for the linear elasticity equations in highly heterogeneous and high contrast…
We propose a new method, the continuous Galerkin method with globally and locally supported basis functions (CG-GL), to address the parametric robustness issues of reduced-order models (ROMs) by incorporating solution-based adaptivity with…
In this paper, we present two adaptive methods for the basis enrichment of the mixed Generalized Multiscale Finite Element Method (GMsFEM) for solving the flow problem in heterogeneous media. We develop an a-posteriori error indicator which…
Online enrichment is the extension of a reduced solution space based on the solution of the reduced model. Procedures for online enrichment were published for many localized model order reduction techniques. We show that residual based…
In this paper, we develop an online basis enrichment method with the mortar mixed finite element method, using the oversampling technique, to solve for flow problems in highly heterogeneous media. We first compute a coarse grid solution…
In this paper, we consider an online basis enrichment mixed generalized multiscale method with oversampling, for solving flow problems in highly heterogeneous porous media. This is an exten- sion of the online mixed generalized multiscale…
There has been an arising trend of adopting deep learning methods to study partial differential equations (PDEs). This article is to propose a Deep Learning Galerkin Method (DGM) for the closed-loop geothermal system, which is a new coupled…
In this work, we introduce a generalization of the enriched Galerkin (EG) method. The key feature of our scheme is an adaptive two-mesh approach that, in addition to the standard enrichment of a conforming finite element discretization via…
In this paper, we develop an iterative scheme to construct multiscale basis functions within the framework of the Constraint Energy Minimizing Generalized Multiscale Finite Element Method (CEM-GMsFEM) for the mixed formulation. The…
In this paper, we propose an adaptive approach, based on mesh refinement or parametric enrichment with polynomial degree adaption, for numerical solution of convection dominated equations with random input data. A parametric system emerged…
We present a robust and efficient target-based mesh adaptation methodology, building on hybridized discontinuous Galerkin schemes for (nonlinear) convection-diffusion problems, including the compressible Euler and Navier-Stokes equations.…