Related papers: Approximation Capabilities of Immersed Finite Elem…
In this paper, we propose a linear and monolithic finite element method for the approximation of an incompressible viscous fluid interacting with an elastic and deforming plate. We use the arbitrary Lagrangian-Eulerian (ALE) approach that…
We present a new type of triangular $C^1$ finite elements developed for the plane strain crack problems within the simplified strain gradient elasticity (SGE). The finite element space contains a conventional fifth-degree polynomial…
We present a finite-element software library, IRENE, which allows to solve numerically the dynamics of a viscous fluid layer embedded in three-dimensional space. Unlike finite-element libraries present in the literature, IRENE can handle…
When solving elliptic partial differential equations in a region containing immersed interfaces (possibly evolving in time), it is often desirable to approximate the problem using an independent background discretisation, not aligned with…
A computationally efficient method is presented for approximate optimization of cutting pattern of frame-supported and pneumatic membrane structures. The plane cutting sheet is generated by minimizing the error from the shape obtained by…
Finite element spaces by Whitney $k$-forms on cubical meshes in $\mathbb{R}^n$ are presented. Based on the spaces, compatible discretizations to $H\Lambda^k$ problems are provided, and discrete de Rham complexes and commutative diagrams are…
A unified construction of high order shape functions is given for all four classical energy spaces ($H^1$, $H(\mathrm{curl})$, $H(\mathrm{div})$ and $L^2$) and for elements of "all" shapes (segment, quadrilateral, triangle, hexahedron,…
We construct finite element subspaces of the space of symmetric tensors with square-integrable divergence on a three-dimensional domain. These spaces can be used to approximate the stress field in the classical Hellinger--Reissner mixed…
We study some numerical methods for solving second order elliptic problem with interface. We introduce an immersed interface finite element method based on the `broken' $P_1$-nonconforming piecewise linear polynomials on interface…
We study an elliptic interface problem with discontinuous diffusion coefficients on unfitted meshes using the CutFEM method. Our main contribution is the reconstruction of conservative fluxes from the CutFEM solution and their use in a…
In this paper, we present a new polygonal finite element method, called the Zipped Finite Element Method, for star-shaped polygons. The proposed approach constructs high-order shape functions as linear combinations of standard finite…
In the context of unfitted finite element discretizations the realization of high order methods is challenging due to the fact that the geometry approximation has to be sufficiently accurate. Recently a new unfitted finite element method…
Fluid-structure systems occur in a range of scientific and engineering applications. The immersed boundary(IB) method is a widely recognized and effective modeling paradigm for simulating fluid-structure interaction(FSI) in such systems,…
In this communication the advantages and drawbacks of the isogeometric analysis (IGA) are reviewed in the context of electromagnetic simulations. IGA extends the set of polynomial basis functions, commonly employed by the classical Finite…
In this work, we investigate the performance CutFEM as a high fidelity solver as well as we construct a competent and economical reduced order solver for PDE-constrained optimization problems in parametrized domains that live in a fixed…
For the finite element simulation of thin soft biological tissues in dynamics, shell elements, compared to volume elements, can capture the whole tissue thickness at once, and feature larger critical time steps. However, the capabilities of…
We present an elastic simulator for domains defined as evolving implicit functions, which is efficient, robust, and differentiable with respect to both shape and material. This simulator is motivated by applications in 3D reconstruction: it…
This paper presents a novel exact finite element formulation of quasi-3D beam for high-fidelity analysis of functionally graded sandwich beams. Unlike conventional displacement-based elements that rely on approximate interpolation functions…
The recently proposed soft finite element method (SoftFEM) reduces the stiffness (condition numbers), consequently improving the overall approximation accuracy. The method subtracts a least-square term that penalizes the gradient jumps…
This paper presents a general, nonlinear isogeometric finite element formulation for rotation-free shells with embedded fibers that captures anisotropy in stretching, shearing, twisting and bending -- both in-plane and out-of-plane. These…