This paper derives a posteriori error estimates for conforming numerical approximations of the Laplace eigenvalue problem with a homogeneous Dirichlet boundary condition. In particular, upper and lower bounds for an arbitrary simple eigenvalue are given. These bounds are guaranteed, fully computable, and converge with optimal speed to the given exact eigenvalue. They are valid without restricti...

This note summarizes the results in [1, 3, 2] on the construction of parallel local multigrid methods. In addition, we present an extended formalization of the adaptive data structure in order to describe precisely the requirements for adaptive multigrid methods with local smoothing for general finite element discretizations. Based on this formalization algorithms can be defined, developed, and...

This paper introduces a new variational formulation for Dirichlet boundary control problem of elliptic partial differential equations, based on observations that the state and adjoint are related through domain, such relation may be imposed in state. Well-posedness (unique solvability stability) is established $H^{1}(\Omega)\times H_{0}^{1}(\Omega)$ space respective A finite element method this...

Bonded multi-material assemblies arise frequently in design, manufacturing, architecture, and materials design. It is a common wisdom that finite element analysis of such assemblies usually requires all components to be represented by compatible finite element meshes; application of meshfree methods in such situations is often considered problematic due to the need to impose additional interfac...

The past decades have witnessed an increasing interest in numerical simulation for flow fractured porous media. To date, most studies focused on 2D or pseudo-3D computational models, where the impact of 3D complex structures seepage has not been fully addressed. This work presents a method modeling heterogeneous structures, typically stochastic discrete fractures and inclusions, are able to be ...

Developments in the field of parametrization-based quad mesh generation on surfaces have been impactful over past decade. In this context, an important advance has replacement error-prone rounding integer-grid maps, by robust quantization methods. parallel, hex for volumes advanced. volumetric however, state-of-the-art still relies fragile rounding, not rarely producing defective meshes, especi...

The behaviour of liquids and gases ranks among the most familiar and yet complex physical phenomena commonly encountered in daily life. To create a seamless approximation of the real world, it is clear that we must be able to accurately simulate fluids. However, a crucial element of what makes fluid behaviour so complex and compelling is its interactions with its surroundings. To simulate the m...

An implicit finite-element flow solver based on the Galerkin finite-element method is employed to study unsteady laminar flow past single and multiple objects. A fast dynamic remeshing technique is used to control the distribution of the mesh nodes during the unsteady simulation, thus minimizing (or even eliminating) the need for adding artificial dissipation terms. The quad-dominant mesh gener...

In this paper, an adaptive mesh refinement technique is developed and analyzed for the non-conforming immersed finite element (IFE) method proposed in [27]. The IFE method was developed for solving the second order elliptic boundary value problem with interfaces across which the coefficient may be discontinuous. The IFE method was based on a triangulation that does not need to fit the interface...

Abstract Finite element methods for heat simulation at urban scale require mesh-volume models, where the meshing process requires a special attention in order to satisfy FEM requirements. In this paper we propose procedural volume modeling approach automatic creation of buildings, which are suitable simulations scale. We develop basic rule-set library and building generation procedure that guar...