Related papers: Finite element method with local damage on the mes…
We introduce an adaptive superconvergent finite element method for a class of mixed formulations to solve partial differential equations involving a diffusion term. It combines a superconvergent postprocessing technique for the primal…
In this article we study adaptive finite element methods (AFEM) with inexact solvers for a class of semilinear elliptic interface problems. We are particularly interested in nonlinear problems with discontinuous diffusion coefficients, such…
The state-of-the art proof of a global inf-sup condition on mixed finite element schemes does not allow for an analysis of truly indefinite, second-order linear elliptic PDEs. This paper, therefore, first analyses a nonconforming finite…
We analyze optimal complexity of adaptive finite element methods (AFEMs) for general second-order linear elliptic partial differential equations (PDEs) in the Lax-Milgram setting. To this end, we formulate an adaptive algorithm which steers…
We formulate and analyze a goal-oriented adaptive finite element method for a symmetric linear elliptic partial differential equation (PDE) that can simultaneously deal with multiple linear goal functionals. In each step of the algorithm,…
We consider mixed finite element methods for linear elasticity where the symmetry of the stress tensor is weakly enforced. Both an a priori and a posteriori error analysis are given for several known families of methods that are uniformly…
Finite element methods provide accurate and efficient methods for the numerical solution of partial differential equations by means of restricting variational problems to finite-dimensional approximating spaces. However, they do not…
In this paper, we develop an adaptive finite element method for the nonlinear steady-state Poisson-Nernst-Planck equations, where the spatial adaptivity for geometrical singularities and boundary layer effects are mainly considered. As a…
We develop a finite element method for elliptic partial differential equations on so called composite surfaces that are built up out of a finite number of surfaces with boundaries that fit together nicely in the sense that the intersection…
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…
Mesh sensitivity of finite element solution for linear elliptic partial differential equations is analyzed. A bound for the change in the finite element solution is obtained in terms of the mesh deformation and its gradient. The bound shows…
In this paper we develop a simple finite element method for simulation of embedded layers of high permeability in a matrix of lower permeability using a basic model of Darcy flow in embedded cracks. The cracks are allowed to cut through the…
Mesh optimization procedures are generally a combination of node smoothing and discrete operations which affect a small number of elements to improve the quality of the overall mesh. These procedures are useful as a post-processing step in…
With the development of multi-layer elastic systems in the field of engineering mechanics, the corresponding variational inequality theory and algorithm design have received more attention and research. In this study, a class of equivalent…
This note constructs a local generalized finite element basis for elliptic problems with heterogeneous and highly varying coefficients. The basis functions are solutions of local problems on vertex patches. The error of the corresponding…
A simple and efficient interface-fitted mesh generation algorithm is developed in this paper. This algorithm can produce a local anisotropic fitting mixed mesh which consists of both triangles and quadrilaterals near the interface. A new…
We consider a one-dimensional fracture problem modelled using either the phase-field or lip-field approach. In both cases, we optimise the incremental potential with respect to the displacement and damage fields and the nodal coordinates of…
A type of adaptive finite element method for the eigenvalue problems is proposed based on the multilevel correction scheme. In this method, adaptive finite element method to solve eigenvalue problems involves solving associated boundary…
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…
We consider the least-squares finite element method (lsfem) for systems of nonlinear ordinary differential equations and establish an optimal error estimate for this method when piecewise linear elements are used. The main assumptions are…