Related papers: An efficient finite element method for computing t…
Well-conditioned boundary integral methods for the solution of elliptic boundary value problems (BVPs) are powerful tools for static and dynamic physical simulations. When there are many close-to-touching boundaries (eg, in complex fluids)…
We combine the parameterization method for invariant manifolds with the finite element method for elliptic PDEs,to obtain a new computational framework for high order approximation of invariant manifolds attached to unstable equilibrium…
A high order cut finite element method is formulated for solving the elastic wave equation. Both a single domain problem and an interface problem are treated. The boundary or interface are allowed to cut through the background mesh. To…
This paper studies formulations of second-order elliptic partial differential equations in nondivergence form on convex domains as equivalent variational problems. The first formulation is that of Smears \& S\"uli [SIAM J.\ Numer.\ Anal.\…
In this paper, a three-dimensional numerical solver is developed for suspensions of rigid and soft particles and droplets in viscoelastic and elastoviscoplastic (EVP) fluids. The presented algorithm is designed to allow for the first time…
In this work we develop and analyze an adaptive finite element method for efficiently solving electrical impedance tomography -- a severely ill-posed nonlinear inverse problem for recovering the conductivity from boundary voltage…
This article presents a $P_0$ finite element method for boundary value problems for linear elasticity equations. The new method makes use of piecewise constant approximating functions on the boundary of each polytopal element, and is…
In this paper, we study adaptive finite element approximations in a perturbation framework, which makes use of the existing adaptive finite element analysis of a linear symmetric elliptic problem. We prove the convergence and complexity of…
In arXiv:2307.03503 [math.NA] we commenced to study a variant of the Raviart-Thomas mixed finite element method for triangles, to solve second order elliptic equations in a curved domain with Neumann or mixed boundary conditions. It is well…
The Virtual Element Method (VEM) is a well-established framework for solving partial differential equations on polygonal and polyhedral meshes. In this paper, we introduce a novel hybrid VEM that integrates both conforming and nonconforming…
The aim of this paper is to propose an efficient adaptive finite element method for eigenvalue problems based on the multilevel correction scheme and inverse power method. This method involves solving associated boundary value problems on…
We present two approaches to constructing isoparametric Virtual Element Methods of arbitrary order for linear elliptic partial differential equations on general two-dimensional domains. The first method approximates the variational problem…
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…
In this paper, we employ the linear virtual element spaces to discretize the semilinear sine-Gordon equation in two dimensions. The salient features of the virtual element method (VEM) are: (a) it does not require explicit form of the shape…
A novel boundary element method (BEM) removes the classical dependence on explicit fundamental solutions and extends quasi-optimal BEM discretisations to strongly elliptic operators with variable coefficients. The approach constructs a…
We study the discretization of an elliptic partial differential equation, posed on a two- or three-dimensional domain with smooth boundary, endowed with a generalized Robin boundary condition which involves the Laplace-Beltrami operator on…
The proximal Galerkin finite element method is a high-order, low-iteration complexity, nonlinear numerical method that preserves the geometric and algebraic structure of point-wise bound constraints in infinite-dimensional function spaces.…
The automated finite element analysis of complex CAD models using boundary-fitted meshes is rife with difficulties. Immersed finite element methods are intrinsically more robust but usually less accurate. In this work, we introduce an…
The immersed boundary-finite element method (IBFE) is an approach to describing the dynamics of an elastic structure immersed in an incompressible viscous fluid. In this formulation, there are discontinuities in the pressure and viscous…
We present a finite element scheme for fractional diffusion problems with varying diffusivity and fractional order. We consider a symmetric integral form of these nonlocal equations defined on general geometries and in arbitrary bounded…