Related papers: Non-conforming finite elements on polytopal meshes
We develop a general convergence theory for adaptive discontinuous Galerkin methods for elliptic PDEs covering the popular SIPG, NIPG and LDG schemes as well as all practically relevant marking strategies. Another key feature of the…
We present a Total Lagrangian finite element framework for finite-deformation multibody dynamics. The framework combines a compact kinematic representation, a deformation-gradient-based formulation, an element-agnostic constitutive…
We analyze adaptive mesh-refining algorithms for conforming finite element discretizations of certain non-linear second-order partial differential equations. We allow continuous polynomials of arbitrary, but fixed polynomial order. The…
We design an adaptive unfitted finite element method on the Cartesian mesh with hanging nodes. We derive an hp-reliable and efficient residual type a posteriori error estimate on K-meshes. A key ingredient is a novel hp-domain inverse…
This paper constructs the first mixed finite element for the linear elasticity problem in 3D using $P_3$ polynomials for the stress and discontinuous $P_2$ polynomials for the displacement on tetrahedral meshes under some mild mesh…
A novel mass-lumping strategy for a mixed finite element approximation of Maxwell's equations is proposed. On structured orthogonal grids the resulting method coincides with the spatial discretization of the Yee scheme. The proposed method,…
In this article we develop convergence theory for a general class of adaptive approximation algorithms for abstract nonlinear operator equations on Banach spaces, and use the theory to obtain convergence results for practical adaptive…
The favored phase field method (PFM) has encountered challenges in the finite strain fracture modeling of nearly or truly incompressible hyperelastic materials. We identified that the underlying cause lies in the innate contradiction…
This paper presents an integrated framework to construct local-energy solutions to fairly general nonlinear diffusion equations for initial data growing at infinity under suitable assumptions on local-energy estimates for approximate…
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…
Stiffness degradation and progressive failure of composite laminates are complex processes involving evolution and multi-mode interactions among fiber fractures, intra-ply matrix cracks and inter-ply delaminations. This paper presents a…
A new discontinuous Galerkin finite element method for the Stokes equations is developed in the primary velocity-pressure formulation. This method employs discontinuous polynomials for both velocity and pressure on general…
A nonlinear Helmholtz equation (NLH) with high wave number and Sommerfeld radiation condition is approximated by the perfectly matched layer (PML) technique and then discretized by the linear finite element method (FEM).…
We propose a high order unfitted finite element method for solving timeharmonic Maxwell interface problems. The unfitted finite element method is based on a mixed formulation in the discontinuous Galerkin framework on a Cartesian mesh with…
In this paper we propose simple multiscale basis functions with constraint energy minimization to solve elliptic problems with high contrast medium. Our methodology is based on the recently developed non-local multicontinuum method (NLMC).…
Immersed finite element methods provide a convenient analysis framework for problems involving geometrically complex domains, such as those found in topology optimization and microstructures for engineered materials. However, their…
Elliptic partial differential equations (PDEs) with discontinuous diffusion coefficients occur in application domains such as diffusions through porous media, electro-magnetic field propagation on heterogeneous media, and diffusion…
We present a finite element discretisation to model the interaction between a poroelastic structure and an elastic medium. The consolidation problem considers fully coupled deformations across an interface, ensuring continuity of…
We present a weak finite element method for elliptic problems in one space dimension. Our analysis shows that this method has more advantages than the known weak Galerkin method proposed for multi-dimensional problems, for example, it has…
A new weak Galerkin (WG) finite element method for solving the second-order elliptic problems on polygonal meshes by using polynomials of boundary continuity is introduced and analyzed. The WG method is utilizing weak functions and their…