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In this paper, new unfitted mixed finite elements are presented for elliptic interface problems with jump coefficients. Our model is based on a fictitious domain formulation with distributed Lagrange multiplier. The relevance of our…
An adaptive finite element method is presented for the elastic scattering of a time-harmonic plane wave by a periodic surface. First, the unbounded physical domain is truncated into a bounded computational domain by introducing the…
In this paper, we study an adaptive finite element method for a class of a nonlinear eigenvalue problems that may be of nonconvex energy functional and consider its applications to quantum chemistry. We prove the convergence of adaptive…
We propose a novel finite element method scheme for singularly perturbed advection-diffusion-reaction problems, which combines certain quantum-assisted stabilization scheme with a classical h-adaptive approach to provide automatic error…
In this paper, we study an adaptive finite element method for multiple eigenvalue problems of a class of second order elliptic equations. By using some eigenspace approximation technology and its crucial property which is also presented in…
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…
An adaptive moving mesh finite element method is studied for the numerical solution of the porous medium equation with and without variable exponents and absorption. The method is based on the so-called moving mesh partial differential…
As inelastic structures are ubiquitous in many engineering fields, a central task in computational mechanics is to develop accurate, robust and efficient tools for their analysis. Motivated by the poor performances exhibited by standard…
In this article we prove that it is possible to construct, using newest-vertex bisection, meshes that equidistribute the error in $H^1$-norm, whenever the function to approximate can be decomposed as a sum of a regular part plus a singular…
In this paper we prove the optimal convergence of a standard adaptive scheme based on edge finite elements for the approximation of the solutions of the eigenvalue problem associated with Maxwell's equations. The proof uses the known…
The paper develops a finite element method for partial differential equations posed on hypersurfaces in $\mathbb{R}^N$, $N=2,3$. The method uses traces of bulk finite element functions on a surface embedded in a volumetric domain. The bulk…
We consider a mixed finite element method for approximating the solution of nearly incompressible elasticity and Stokes equations. The finite element method is based on quadrilateral and hexahedral triangulation using primal and dual…
The eXtended Finite Element Method (XFEM) is used to solve interface problems with an unfitted mesh. We present an implementation of the XFEM in the FEM-library deal.II. The main parts of the implementation are (i) the appropriate…
This article considers a model problem of elastoplasticity with linearly kinematic hardening and presents hp-finite element discretizations of two equivalent weak formulations each having their respective advantages. A mixed variational…
In this paper, we present a unified analysis of both convergence and optimality of adaptive mixed finite element methods for a class of problems when the finite element spaces and corresponding a posteriori error estimates under…
This work describes a concise algorithm for the generation of triangular meshes with the help of standard adaptive finite element methods. We demonstrate that a generic adaptive finite element solver can be repurposed into a triangular mesh…
This paper proposes a finite element method that couples mixed and Lagrange finite elements to efficiently capture stress concentrations in elasticity problems. The method employs conforming mixed finite elements in regions with stress…
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…
We present higher-order piecewise continuous finite element methods for solving a class of interface problems in two dimensions. The method is based on correction terms added to the right-hand side in the standard variational formulation of…
In this work, we consider unfitted finite element methods for the numerical approximation of the Stokes problem. It is well-known that this kind of methods lead to arbitrarily ill-conditioned systems. In order to solve this issue, we…