We present Laguerre Voronoi based subdivision algorithms for the quadrilateral and hexahedral meshing of particle systems within a bounded region in two and three dimensions, respectively. Particles are smooth functions over circular or spherical domains. The algorithm first breaks the bounded region containing the particles into Voronoi cells that are then subsequently decomposed into an initi...

We introduce and analyze a mixed finite element method for the numerical discretization of a stationary incompressible magnetohydrodynamics problem, in two and three dimensions. The velocity field is discretized using divergence-conforming Brezzi-Douglas-Marini (BDM) elements and the magnetic field is approximated by curl-conforming Nédélec elements. The H1-continuity of the velocity field is e...

This paper studies a new recovery-based a posteriori error estimator for the conforming linear finite element approximation to elliptic interface problems. Instead of recovering the gradient in the continuous finite element space, the flux is recovered through a weighted L2 projection onto H(div) conforming finite element spaces. The resulting error estimator is analyzed by establishing the rel...

In this paper, we discuss the formulation, stability and validation of a high-order non-dissipative discontinuous Galerkin (DG) method for solving Maxwell’s equations on non-conforming simplex meshes. The proposed method combines a centered approximation for the numerical fluxes at inter element boundaries, with either a second-order or a fourth-order leap-frog time integration scheme. Moreover...

This work is concerned with the design of a hp-like discontinuous Galerkin (DG) method for solving the two-dimensional time-domain Maxwell equations on non-conforming locally refined triangular meshes. The proposed DG method allows non-conforming meshes with arbitrary-level hanging nodes. This method combines a centered approximation for the evaluation of fluxes at the interface between neighbo...

The mortar finite element is an example of a non-conforming method which can be used to decompose and re-compose a domain into subdomains without requiring compatibility between the meshes on the separate components. We obtain stability and convergence results for this method that are uniform in terms of both the degree and the mesh used, without assuming quasiuniformity for the meshes. Our res...

Abstract We derive an anisotropic a posteriori error estimate for the adaptive conforming virtual element approximation of paradigmatic two-dimensional elliptic problem. In particular, we introduce quasi-interpolant operator and exploit its results to prove reliability indicator. design implement corresponding polygonal algorithm. Several numerical tests assess superiority proposed algorithm in...

STUDY DESIGN A comprehensive systematic review of the literature. OBJECTIVES To assess the modern literature on the use of polyethylene mesh-contained morcelized allograft (PMCMA) bone for spinal fusion and vertebral compression fracture management. SUMMARY OF BACKGROUND DATA There are presently no systematic reviews of PMCMA. METHODS A systematic literature review was performed within th...

We construct mesh-independent and parameter-robust monolithic solvers for the coupled primal Stokes--Darcy problem. Three different formulations their discretizations in terms of conforming nonconforming finite element methods volume are considered. In each case, robust preconditioners derived using a unified theoretical framework. particular, suggested utilize operators fractional Sobolev spac...

In this paper we study the finite element approximation of systems second-order nonlinear hyperbolic equations. The proposed numerical method combines a hp -version discontinuous Galerkin in time direction with an H 1 (Ω)-conforming spatial variables. Error bounds at temporal nodal points are derived under weak restriction on step size terms mesh size. Numerical experiments presented to verify ...