Related papers: An Adaptive Finite Element DtN Method for the Acou…
We present an adaptive finite element method for the incompressible Navier--Stokes equations based on a standard splitting scheme (the incremental pressure correction scheme). The presented method combines the efficiency and simplicity of a…
We present a finite element discretisation to model the interaction between a poroelastic structure and an elastic medium. The consolidation problem considers fully coupled deformations across an interface, ensuring continuity of…
We investigate the potential of applying (D)NN ((deep) neural networks) for approximating nonlinear mappings arising in the finite element discretization of nonlinear PDEs (partial differential equations). As an application, we apply the…
In the context of non overlapping domain decomposition methods, several algebraic approximations of the Dirichlet-to-Neumann (DtN) map are proposed in [F. X. Roux, et. al. Algebraic approximation of Dirichlet- to-Neumann maps for the…
Finite difference method and pseudo-spectral method have been widely used in the numerical relativity to solve the Einstein equations. As the third major category method to solve partial differential equations, finite element method is much…
An adaptive regularization strategy for stabilizing Newton-like iterations on a coarse mesh is developed in the context of adaptive finite element methods for nonlinear PDE. Existence, uniqueness and approximation properties are known for…
In this paper, a two-dimensional Dirichlet-to-Neumann (DtN) finite element method (FEM) is developed to analyze the scattering of SH guided waves due to an interface delamination in a bi-material plate. During the finite element analysis,…
In this paper, we describe a stable finite element formulation for advection-diffusion-reaction problems that allows for robust automatic adaptive strategies to be easily implemented. We consider locally vanishing, heterogeneous, and…
Metasurfaces are extremely useful for controlling and manipulating electromagnetic waves. Full-wave numerical simulation is highly desired for their design and optimization, but it is notoriously difficult, even for two-dimensional…
This paper details the development and application of an $h$-adaptive finite element method for the numerical solution of the \textit{Falkner-Skan equation}. A posteriori error estimation governs the adaptivity of the mesh, specifically the…
Investigating the sound field in and around ducts is an important topic in acoustics, e.g. when simulating musical instruments or the human vocal tract. In this paper a method that is based on the boundary element method in 3D combined with…
In this paper we propose a finite element method for solving elliptic equations with the observational Dirichlet boundary data which may subject to random noises. The method is based on the weak formulation of Lagrangian multiplier. We show…
A finite element methodology for large classes of variational boundary value problems is defined which involves discretizing two linear operators: (1) the differential operator defining the spatial boundary value problem; and (2) a Riesz…
A systematic study of small, time-dependent, perturbations to geometric wave-equation domains is hardly existent. Acoustic enclosures are typical examples featuring locally reacting surfaces that respond to a pressure gradient or a pressure…
Nonlinear dynamics have long been exploited in order to damp vibrations in solid mechanics. The phenomenon of irreversible energy transfer from a linear primary system to a nonlinear absorber has driven great attention to the optimal design…
A type of adaptive finite element method for the eigenvalue problems is proposed based on the multilevel correction scheme. In this method, adaptive finite element method to solve eigenvalue problems involves solving associated boundary…
In this paper, we discuss problems arising when computing resonances with a finite element method. In the pre-asymptotic regime, we detect for the one dimensional case, spurious solutions in finite element computations of resonances when…
Optimal convergence rates of adaptive finite element methods are well understood in terms of the axioms of adaptivity. One key ingredient is the discrete reliability of a residual-based a posteriori error estimator, which controls the error…
An optimized phonon approach for the numerical diagonalization of interacting electron-phonon systems is proposed. The variational method is based on an expansion in coherent states that leads to a dramatic truncation in the phonon space.…
A nonlinear analysis of high-frequency thickness-shear vibrations of AT-cut quartz crystal plates is presented with the two-dimensional finite element method. We expanded both kinematic and constitutive nonlinear Mindlin plate equations and…