Related papers: Finite Element Methods For Interface Problems On L…
Anisotropic mesh quality measures and anisotropic mesh adaptation are studied for polygonal meshes. Three sets of alignment and equidistribution measures are developed, one based on least squares fitting, one based on generalized…
We present a new framework for expressing finite element methods on multiple intersecting meshes: multimesh finite element methods. The framework enables the use of separate meshes to discretize parts of a computational domain that are…
The conformal formulation of the Einstein constraint equations is first reviewed, and we then consider the design, analysis, and implementation of adaptive multilevel finite element-type numerical methods for the resulting coupled nonlinear…
Fourth-order differential equations play an important role in many applications in science and engineering. In this paper, we present a three-field mixed finite-element formulation for fourth-order problems, with a focus on the effective…
In this paper, we present a new numerical method for determining the numerical solution of interface problems to optimal accuracy with respect to the polynomial order of the Lagrangian finite element space on polytopial meshes. We introduce…
We design an adaptive finite element method to approximate the solutions of quasi-linear elliptic problems. The algorithm is based on a Ka\v{c}anov iteration and a mesh adaptation step is performed after each linear solve. The method is…
An expandable local and parallel two-grid finite element scheme based on superposition principle for elliptic problems is proposed and analyzed in this paper by taking example of Poisson equation. Compared with the usual local and parallel…
Anisotropic mesh adaptation is studied for the linear finite element solution of eigenvalue problems with anisotropic diffusion operators. The M-uniform mesh approach is employed with which any nonuniform mesh is characterized…
This work develops and analyzes a variational-monolithic unfitted finite element formulation of a linear fluid-structure interaction problem in Eulerian coordinates with a fixed interface. The overall discretization is based on a backward…
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 introduce generalised finite difference methods for solving fully nonlinear elliptic partial differential equations. Methods are based on piecewise Cartesian meshes augmented by additional points along the boundary. This allows for…
This article considers the extension of two-grid $hp$-version discontinuous Galerkin finite element methods for the numerical approximation of second-order quasilinear elliptic boundary value problems of monotone type to the case when…
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…
For elliptic interface problems with discontinuous coefficients, the maximum accuracy order for compact 9-point finite difference scheme in irregular points is three [7]. The discontinuous coefficients usually have abrupt jumps across the…
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…
Heterogeneous anisotropic diffusion problems arise in the various areas of science and engineering including plasma physics, petroleum engineering, and image processing. Standard numerical methods can produce spurious oscillations when they…
During design optimization, a smooth description of the geometry is important, especially for problems that are sensitive to the way interfaces are resolved, e.g., wave propagation or fluid-structure interaction. A levelset description of…
Mesh adaptation for finite element approximation is a procedure used in numerous applications. The use of thin and long anisotropic triangles improves the efficiency of the procedure. When piecewise linear finite elements are used, the…
In this paper, a symmetrized two-scale finite element method is proposed for a class of partial differential equations with symmetric solutions. With this method, the finite element approximation on a fine tensor product grid is reduced to…
Despite the rapidly evolving field of computational electromagnetics, few open-source tools have managed to tackle the problem of automatic mesh generation for properly discretizing the problem of interest into a finite set of elements…