Related papers: Higher-order spectral element method for the stati…
We perform stability analyses for discontinuous Galerkin spectral element approximations of linear variable coefficient hyperbolic systems in three dimensional domains with curved elements. Although high order, the precision of the…
In this work we propose, {analyze}, and validate a stabilized finite element method for a flow problem arising from the assessment of {4D Flow Magnetic Resonance Imaging quality}. Starting from the Navier-Stokes equation and splitting its…
In this paper a mixed spectral element formulation is presented for planar, linear elasticity. The degrees of freedom for the stress are integrated traction components, i.e. surface force components. As a result the tractions between…
We prove stability bounds for Stokes-like virtual element spaces in two and three dimensions. Such bounds are also instrumental in deriving optimal interpolation estimates. Furthermore, we develop some numerical tests in order to…
The nonconforming Morley-type virtual element method for the incompressible Navier-Stokes equations formulated in terms of the stream-function on simply connected polygonal domains (not necessarily convex) is designed. A rigorous analysis…
In this thesis, we investigate a novel local projection based stabilized conforming virtual element method for the generalized Oseen problem using equal-order element pairs on general polygonal meshes. To ensure the stability, particularly…
This paper presents an innovative continuous linear finite element approach to effectively solve biharmonic problems on surfaces. The key idea behind this method lies in the strategic utilization of a surface gradient recovery operator to…
We prove convergence of the spectral element method for piecewise polynomial collocation applied to periodic boundary value problems for functional differential equations. In particular, we prove that the numerical collocation solution…
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…
In this paper, we propose and analyse a numerical method to solve 2D Dirichlet time-harmonic elastic wave equations. The procedure is based on the decoupling of the elastic vector field into scalar Pressure ($P$-) and Shear ($S$-) waves via…
Super-convergence of order 1.5 in pressure and velocity has been experimentally investigated for the two-dimensional Stokes problem discretised with the MINI mixed finite element. Even though the classic mixed finite element theory for the…
The immersed boundary method is a numerical and mathematical formulation for solving fluid-structure interaction problems. It relies on solving fluid equations on an Eulerian fluid grid and interpolating the resulting velocity back onto…
This study develops a novel multiscale computational method for heat conduction problems of composite structures with diverse periodic configurations in different subdomains. Firstly, the second-order two-scale (SOTS) solutions for these…
Immersed methods discretize boundary conditions for complex geometries on background Cartesian grids. This makes such methods especially suitable for two-way coupled flow-body problems, where the body mechanics are partially driven by…
This study proposes a high-order multi-scale method tailored for time-dependent nonlinear thermo-electro-mechanical coupling problems of composite structures with highly spatial heterogeneity, which incorporate temperature-dependent…
The aim of this paper is to analyze the influence of small edges in the computation of the spectrum of the Steklov eigenvalue problem by a lowest order virtual element method. Under weaker assumptions on the polygonal meshes, which can…
In this paper, we construct and analyze divergence-free finite element methods for the Stokes problem on smooth domains. The discrete spaces are based on the Scott-Vogelius finite element pair of arbitrary polynomial degree greater than…
In this paper, a direct finite element method is proposed for solving interface problems on unfitted meshes. This new method treats the two interface conditions as an $H^{\frac12}(\Gamma)\times H^{-\frac12}(\Gamma)$ pair for the mutual…
Boundary integral methods are highly suited for problems with complicated geometries, but require special quadrature methods to accurately compute the singular and nearly singular layer potentials that appear in them. This paper presents a…
A two phase elastic composite with weakly compressible elastic inclusions is considered. The homogenised two-scale limit problem is found, via a version of the method of two-scale convergence, and analysed. The microscopic part of the…