Related papers: Multiscale Finite Element Formulations for 2D/1D P…
In this paper, a new type of multi-level correction scheme is proposed for solving eigenvalue problems by finite element method. With this new scheme, the accuracy of eigenpair approximations can be improved after each correction step which…
The paper develops a hybrid method for solving a system of advection--diffusion equations in a bulk domain coupled to advection--diffusion equations on an embedded surface. A monotone nonlinear finite volume method for equations posed in…
Finite element meshes for 3D models simulating realistic malignant melanoma (MM) growth, incorporating accurate dielectric properties of the skin, have been developed. Numerical simulations illustrate how 3D finite element meshes can be…
We develop higher order multipoint flux mixed finite element (MFMFE) methods for solving elliptic problems on quadrilateral and hexahedral grids that reduce to cell-based pressure systems. The methods are based on a new family of mixed…
In this paper, we propose and analyse a numerical method to solve 2D Dirichlet time-harmonic elastic wave equations. The procedure is based on the decoupling of the elastic vector field into scalar Pressure ($P$-) and Shear ($S$-) waves via…
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…
We propose a multiscale method for elliptic problems on complex domains, e.g. domains with cracks or complicated boundary. For local singularities this paper also offers a discrete alternative to enrichment techniques such as XFEM. We…
In this paper, we consider the numerical approximation for a diffuse interface model of the two-phase incompressible inductionless magnetohydrodynamics problem. This model consists of Cahn-Hilliard equations, Navier-Stokes equations and…
Finite element methods usually construct basis functions and quadrature rules for multidimensional domains via tensor products of one-dimensional counterparts. While straightforward, this approach results in integration spaces larger than…
This paper presents a new time-domain finite-element approach for modelling thin sheets with hyperbolic basis functions derived from the well-known steady-state solution of the linear flux diffusion equation. The combination of solutions at…
In order to reduce the computational cost of the simulation of electromagnetic responses in geophysical settings that involve highly heterogeneous media, we develop a multiscale finite volume method with oversampling for the quasi-static…
The Finite Element Method (FEM) is widely used to solve discrete Partial Differential Equations (PDEs) in engineering and graphics applications. The popularity of FEM led to the development of a large family of variants, most of which…
A multilevel correction scheme is proposed to solve defective and nodefective of nonsymmetric partial differential operators by the finite element method. The method includes multi correction steps in a sequence of finite element spaces. In…
In this paper we develop magnetic induction conforming multiscale formulations for magnetoquasistatic problems involving periodic materials. The formulations are derived using the periodic homogenization theory and applied within a…
Large-scale 3D martensitic microstructure evolution problems are studied using a finite-element discretization of a finite-strain phase-field model. The model admits an arbitrary crystallography of transformation and arbitrary elastic…
Local multiscale methods often construct multiscale basis functions in the offline stage without taking into account input parameters, such as source terms, boundary conditions, and so on. These basis functions are then used in the online…
We propose a novel cut finite element method for the numerical solution of the Biot system of poroelasticity. The Biot system couples elastic deformation of a porous solid with viscous fluid flow and commonly arises on domains with complex…
The paper presents a two-dimensional geometrically nonlinear formulation of a beam element that can accommodate arbitrarily large rotations of cross sections. The formulation is based on the integrated form of equilibrium equations, which…
In this work we propose, {analyze}, and validate a stabilized finite element method for a flow problem arising from the assessment of {4D Flow Magnetic Resonance Imaging quality}. Starting from the Navier-Stokes equation and splitting its…
In this paper, we consider the numerical solution of poroelasticity problems that are of Biot type and develop a general algorithm for solving coupled systems. We discuss the challenges associated with mechanics and flow problems in…