相关论文: Adaptive stabilized finite elements via residual m…
Discretizing a solution in the Fourier domain rather than the time domain presents a significant advantage in solving transport problems that vary smoothly and periodically in time, such as cardiorespiratory flows. The finite element…
The paper introduces an adaptive version of the stabilized Trace Finite Element Method (TraceFEM) designed to solve low-regularity elliptic problems on level-set surfaces using a shape-regular bulk mesh in the embedding space. Two…
We propose a novel finite element method scheme for singularly perturbed advection-diffusion-reaction problems, which combines certain quantum-assisted stabilization scheme with a classical h-adaptive approach to provide automatic error…
For the simulation of rectilinearly moving conductors across a magnetic field, the Galer-kin finite element method (GFEM) is generally employed. The inherent instability of GFEM is very often addressed by employing Streamline…
We propose, analyze mathematically, and study numerically a novel approach for the finite element approximation of the spectrum of second-order elliptic operators. The main idea is to reduce the stiffness of the problem by subtracting a…
We introduce the concept of data-driven finite element methods. These are finite-element discretizations of partial differential equations (PDEs) that resolve quantities of interest with striking accuracy, regardless of the underlying mesh…
In this note, we develop a new stabilization mechanism for cut finite element methods that generalizes previous approaches of ghost penalty type in two ways: (1) The quantity that is stabilized and (2) The choice of elements that are…
We propose using machine learning and artificial neural networks (ANNs) to enhance residual-based stabilization methods for advection-dominated differential problems. Specifically, in the context of the finite element method, we consider…
We consider a randomised implementation of the finite element method (FEM) for elliptic partial differential equations on high-dimensional models. This is motivated by applications where model predictions are essential for real-time process…
We introduce an automatic variationally stable analysis (AVS) for finite element (FE) computations of scalar-valued convection-diffusion equations with non-constant and highly oscillatory coefficients. In the spirit of least squares FE…
From a mathematical perspective, the extraordinary properties of metamaterials are often reflected in the coefficients of the governing partial differential equations (PDEs). These coefficients may fall outside the assumptions of classical…
We equip a high-order continuous Galerkin discretization of a general hyperbolic problem with a nonlinear stabilization term and introduce a new methodology for enforcing preservation of invariant domains. The amount of shock-capturing…
We consider locally stabilized, conforming finite element schemes on completely unstructured simplicial space-time meshes for the numerical solution of parabolic initial-boundary value problems with variable, possibly discontinuous in space…
We compare several stabilization methods in the context of isogeometric analysis and B-spline basis functions, using an advection-dominated advection\revision{-}diffusion as a model problem. We derive (1) the least-squares finite element…
We present a methodology combining neural networks with physical principle constraints in the form of partial differential equations (PDEs). The approach allows to train neural networks while respecting the PDEs as a strong constraint in…
The subject of this work is an adaptive stochastic Galerkin finite element method for parametric or random elliptic partial differential equations, which generates sparse product polynomial expansions with respect to the parametric…
Motivated by applications to numerical simulation of flows in highly heterogeneous porous media, we develop multiscale finite element methods for second order elliptic equations. We discuss a multiscale model reduction technique in the…
In this work, we propose a bi-grid scheme framework for the Allen-Cahn equation in Finite Element Method. The new methods are based on the use of two FEM spaces, a coarse one and a fine one, and on a decomposition of the solution into mean…
We present a full space-time numerical solution of the advection-diffusion equation using a continuous Galerkin finite element method on conforming meshes. The Galerkin/least-square method is employed to ensure stability of the discrete…
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…