Related papers: Space-time boundary elements for frictional contac…
We develop a new finite element method for solving planar elasticity problems involving of heterogeneous materials with a mesh not necessarily aligning with the interface of the materials. This method is based on the `broken'…
Elastic interaction of pressurized spherical cavities embedded in a three-dimensional hyperelastic medium is computationally analyzed. Using finite element analysis across several positive and negative pressure scenarios, we calculate the…
We consider a scalar valued elliptic partial differential equation on a sufficiently smooth domain $\Omega$, subject to a regularized Tresca friction-type boundary condition on a subset $\Gamma$ of $\partial \Omega$. The friction threshold,…
This work is concerned with the analysis of a space-time finite element discontinuous Galerkin method on polytopal meshes (XT-PolydG) for the numerical discretization of wave propagation in coupled poroelastic-elastic media. The…
This work develops an epsilon-uniform finite element method for singularly perturbed boundary value problems. A surprising and remarkable observation is illustrated: By moving one node arbitrarily in between its adjacent nodes, the new…
The paper introduces a new finite element numerical method for the solution of partial differential equations on evolving domains. The approach uses a completely Eulerian description of the domain motion. The physical domain is embedded in…
In this paper we formulate and analyze a space-time finite element method for the numerical simulation of rotating electric machines where the finite element mesh is fixed in space-time domain. Based on the Babu\v{s}ka--Ne\v{c}as theory we…
A self-consistent theory for the classical description of the interaction of light and matter at the nano-scale is presented, which takes into account spatial dispersion. Up to now, the Maxwell equations in nanostructured materials with…
This thesis deals with shape optimization for contact mechanics. More specifically, the linear elasticity model is considered under the small deformations hypothesis, and the elastic body is assumed to be in contact (sliding or with Tresca…
A finite element approximation of the Stokes equations under a certain nonlinear boundary condition, namely, the slip or leak boundary condition of friction type, is considered. We propose an approximate problem formulated by a variational…
We explore the recently-proposed Virtual Element Method (VEM) for numerical solution of boundary value problems on arbitrary polyhedral meshes. More specifically, we focus on the elasticity equations in three-dimensions and elaborate upon…
A discontinuous Petrov-Galerkin (DPG) method is used to solve the time-harmonic equations of linear viscoelasticity. It is based on a "broken" primal variational formulation, which is very similar to the classical primal variational…
The objective of this work is the development of a novel finite element formulation describing the contact interaction of slender beams in complex 3D configurations involving arbitrary beam-to-beam orientations. It is shown in a…
Finite element methods provide accurate and efficient methods for the numerical solution of partial differential equations by means of restricting variational problems to finite-dimensional approximating spaces. However, they do not…
Rigid particles in a Stokesian fluid can physically not overlap, as a thin layer of fluid always separates a particle pair, exerting increasingly strong repulsive forces on the bodies for decreasing separations. Numerically, resolving these…
This study numerically investigated the friction of viscoelastic objects with grooves. A 3D viscoelastic block with grooves on a rigid substrate is slowly pushed from the lateral side under uniform pressure on the top surface. The local…
This paper establishes finite-time splash singularity formation for 3D viscous incompressible neo-Hookean elastodynamics with free boundaries. The system features mixed stress-kinematic conditions where viscous-elastic stresses balance…
We present a new variational principle for the gyrokinetic system, similar to the Maxwell-Vlasov action presented in Ref. 1. The variational principle is in the Eulerian frame and based on constrained variations of the phase space fluid…
We develop a space-time mortar mixed finite element method for parabolic problems. The domain is decomposed into a union of subdomains discretized with non-matching spatial grids and asynchronous time steps. The method is based on a…
This paper deals with a one-dimensional wave equation being subjected to a unilateral boundary condition. An approximation of this problem combining the finite element and mass redistribution methods is proposed. The mass redistribution…