Related papers: A stabilized nonconforming finite element method f…
The paper studies a geometrically unfitted finite element method (FEM), known as trace FEM or cut FEM, for the numerical solution of the Stokes system posed on a closed smooth surface. A trace FEM based on standard Taylor-Hood (continuous…
We combine the parameterization method for invariant manifolds with the finite element method for elliptic PDEs,to obtain a new computational framework for high order approximation of invariant manifolds attached to unstable equilibrium…
We propose and analyze a structure-preserving parametric finite element method (SP-PFEM) for the evolution of closed curves under anisotropic surface diffusion with surface energy density $\hat{\gamma}(\theta)$. Our primary theoretical…
In this paper we apply a nonconforming rotated bilinear tetrahedral element to the Stokes problem in $\mathbb{R}^3$. We show that the element is stable in combination with a piecewise linear, continuous, approximation of the pressure. This…
We present a mixed finite element method with triangular and parallelogram meshes for the Kirchhoff-Love plate bending model. Critical ingredient is the construction of low-dimensional local spaces and appropriate degrees of freedom that…
This paper is concerned with fully discrete finite element methods for approximating variational solutions of nonlinear stochastic elastic wave equations with multiplicative noise. A detailed analysis of the properties of the weak solution…
This paper presents a new mixed finite element method for the Cahn-Hilliard equation. The well-posedness of the mixed formulation is established and the error estimates for its linearized fully discrete scheme are provided. The new mixed…
We develop a micromorphic-based approach for finite element stabilization of reaction-convection-diffusion equations, by gradient enhancement of the field of interest via introducing an auxiliary variable. The well-posedness of the…
We present a wavenumber-explicit convergence analysis of the hp finite element method applied to a class of heterogeneous Helmholtz problems with piecewise analytic coefficients at large wavenumber $k$. Our analysis covers the heterogeneous…
This article presents a higher-order spectral element method for the two-dimensional Stokes interface problem involving a piecewise constant viscosity coefficient. The proposed numerical formulation is based on least-squares formulation.…
We introduce a surface finite element method for the numerical solution of Navier-Stokes equations on evolving surfaces with a prescribed deformation of the surface in normal direction. The method is based on approaches for the full surface…
A finite element approach for approximating the solution of a mathematical model for the response of a penetrable, bounded object (obstacle) to the excitation by an external electromagnetic field is presented and investigated. The model…
Phase transition problems on curved surfaces can lead to a panopticon of fascinating patterns. In this paper we consider finite element approximations of phase field models with a spatially inhomogeneous and anisotropic surface energy…
We propose a generalized finite element method for the strongly damped wave equation with highly varying coefficients. The proposed method is based on the localized orthogonal decomposition introduced and is designed to handle independent…
We develop a theoretical framework for the analysis of stabilized cut finite element methods for the Laplace-Beltrami operator on a manifold embedded in $\mathbb{R}^d$ of arbitrary codimension. The method is based on using continuous…
Convergence results are shown for full discretizations of quasilinear parabolic partial differential equations on evolving surfaces. As a semidiscretization in space the evolving surface finite element method is considered, using a…
A nonconforming $P_3$ finite element is constructed by enriching the conforming $P_3$ finite element space with three $P_3$ nonconforming bubbles and six additional $P_4$ nonconforming bubbles, on each tetrahedron. Here the divergence of…
We derive a residual-based $hp$-a posteriori error estimator for hybrid high-order (HHO) methods on simplicial meshes applied to the biharmonic problem posed on two- and three-dimensional polytopal Lipschitz domains. The a posteriori error…
This paper proposes the response surface method for finite element model updating. The response surface method is implemented by approximating the finite element model surface response equation by a multi-layer perceptron. The updated…
In this paper, we introduce an inertial proximal method for solving a bilevel problem involving two monotone equilibrium bifunctions in Hilbert spaces. Under suitable conditions and without any restrictive assumption on the trajectories,…