Related papers: An arbitrarily high order unfitted finite element …
A new higher-order accurate method is proposed that combines the advantages of the classical $p$-version of the FEM on body-fitted meshes with embedded domain methods. A background mesh composed by higher-order Lagrange elements is used.…
Unfitted finite element techniques are valuable tools in different applications where the generation of body-fitted meshes is difficult. However, these techniques are prone to severe ill conditioning problems that obstruct the efficient use…
New finite element methods are proposed for elliptic interface problems in one and two dimensions. The main motivation is not only to get an accurate solution but also an accurate first order derivative at the interface (from each side).…
We design and analyze a Hybrid High-Order (HHO) method on unfitted meshes to approximate elliptic interface problems. The curved interface can cut through the mesh cells in a very general fashion. As in classical HHO methods, the present…
We present a new fixed mesh algorithm for solving a class of interface inverse problems for the typical elliptic interface problems. These interface inverse problems are formulated as shape optimization prob- lems whose objective…
In this work, we study the design and analysis of a novel hybrid high-order (HHO) method on unfitted meshes. HHO methods rely on a pair of unknowns, combining polynomials attached to the mesh faces and the mesh cells. In the unfitted…
In this work, we bridge standard adaptive mesh refinement and coarsening on scalable octree background meshes and robust unfitted finite element formulations for the automatic and efficient solution of large-scale nonlinear solid mechanics…
This article presents an immersed virtual element method for solving a class of interface problems that combines the advantages of both body-fitted mesh methods and unfitted mesh methods. A background body-fitted mesh is generated…
In this work, we present an adaptive unfitted finite element scheme that combines the aggregated finite element method with parallel adaptive mesh refinement. We introduce a novel scalable distributed-memory implementation of the resulting…
In this paper, we propose a novel high order unfitted finite element method on Cartesian meshes for solving the acoustic wave equation with discontinuous coefficients having complex interface geometry. The unfitted finite element method…
This paper aims to develop an efficient adaptive finite element method for the second-order elliptic problem. Although the theory for adaptive finite element methods based on residual-type a posteriori error estimator and bisection…
This paper presents a high-order method for solving an interface problem for the Poisson equation on embedded meshes through a coupled finite element and integral equation approach. The method is capable of handling homogeneous or…
In this paper, we propose the unfitted spectral element method for solving elliptic interface and corresponding eigenvalue problems. The novelty of the proposed method lies in its combination of the spectral accuracy of the spectral element…
In this paper, we develop and analyze a trilinear immersed finite element method for solving three-dimensional elliptic interface problems. The proposed method can be utilized on interface-unfitted meshes such as Cartesian grids consisting…
In this paper, we present and analyze an unfitted finite element method for the elliptic interface problem. We consider the case that the interface is $C^2$-smooth or polygonal, and the exact solution $u \in H^{1+s}(\Omega_0 \cup \Omega_1)$…
We summarise three applications of the obstacle problem to membrane contact, elastoplastic torsion and cavitation modelling, and show how the resulting models can be solved using mixed finite elements. It is challenging to construct fixed…
When modeling scientific and industrial problems, geometries are typically modeled by explicit boundary representations obtained from computer-aided design software. Unfitted (also known as embedded or immersed) finite element methods offer…
We propose a method that morphs high-orger meshes such that their boundaries and interfaces coincide/align with implicitly defined geometries. Our focus is particularly on the case when the target surface is prescribed as the zero…
This article presents an immersed finite element (IFE) method for solving the typical three-dimensional second order elliptic interface problem with an interface-independent Cartesian mesh. The local IFE space on each interface element…
In this paper we introduce and analyze the residual-based a posteriori error estimation of the partially penalized immersed finite element method for solving elliptic interface problems. The immersed finite element method can be naturally…