Related papers: Addressing Integration Error for Polygonal Finite …
We study the problem of partitioning a given simple polygon $P$ into a minimum number of connected polygonal pieces, each of bounded size. We describe a general technique for constructing such partitions that works for several notions of…
In this work we report some results, obtained within the framework of the ERC Project CHANGE, on the impact on the performance of the virtual element method of the shape of the polygonal elements of the underlying mesh. More in detail,…
Motivated by conforming finite element methods for elliptic problems of second order, we analyze the approximation of the gradient of a target function by continuous piecewise polynomial functions over a simplicial mesh. The main result is…
In the current practices of both industry and academia, the convergence and accuracy of finite element calculations are closely related to the methods and quality of mesh generation. For years, the research on high-quality mesh generation…
The purpose of this research is to describe an efficient iterative method suitable for obtaining high accuracy solutions to high frequency time-harmonic scattering problems. The method allows for both refinement of local polynomial degree…
Equilibrium equations in the form of complementarity conditions often appear as constraints in optimization problems. Problems of this type are commonly referred to as mathematical programs with complementarity constraints (MPCCs). A…
This paper deals with the numerical approximation of the biharmonic inverse source problem in an abstract setting in which the measurement data is finite-dimensional. This unified framework in particular covers the conforming and…
In this paper we construct conforming Virtual Element approximations on domains with curved boundary and/or internal curved interfaces, both in two and three dimensions. Our approach allows to impose both Dirichlet and Neumann…
We define a new finite element method for a steady state elliptic problem with discontinuous diffusion coefficients where the meshes are not aligned with the interface. We prove optimal error estimates in the $L^2$ norm and $H^1$ weighted…
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…
We consider an inverse problem for the linear one-dimensional wave equation with variable coefficients consisting in determining an unknown source term from a boundary observation. A method to obtain approximations of this inverse problem…
Full projector compensation aims to modify a projector input image such that it can compensate for both geometric and photometric disturbance of the projection surface. Traditional methods usually solve the two parts separately, although…
New interpolation and quasi-interpolation operators of Cl\'ement- and Scott-Zhang-type are analyzed on anisotropic polygonal and polyhedral meshes. Since no reference element is available, an appropriate linear mapping to a reference…
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 present solutions to the matrix completion problems proposed by the Alignment Research Center that have a polynomial dependence on the precision $\varepsilon$. The motivation for these problems is to enable efficient computation of…
This paper discusses the split feasibility problem with polynomials. The sets are semi-algebraic, defined by polynomial inequalities. They can be either convex or nonconvex, either feasible or infeasible. We give semidefinite relaxations…
We propose an adaptive polygonal finite element formulation for collapse plastic analysis of solids. The article contributes into four crucial points: 1) Wachspress shape functions at vertex and bubble nodes handled at a primal-mesh level;…
We consider fourth order singularly perturbed eigenvalue problems in one-dimension and the approximation of their solution by the $h$ version of the Finite Element Method (FEM). In particular, we use piecewise Hermite polynomials of degree…
For elliptic interface problems, this paper studies residual-based a posteriori error estimations for various finite element approximations. For the conforming and the Raviart-Thomas mixed elements in two-dimension and for the…
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…