In this paper, we present uniform convergence results for the mortar finite element method (which is an example of a non-conforming method), for h, p and hp discretizations over general meshes. Our numerical and theoretical results show that the mortar finite element method is a good candidate for hp implementation and also that the optimal rates afforded by the conforming h, p and hp discretiz...

Nowadays, with the advances of Finite Element Analysis (FEA) packages, some of the engineering and design problems such as stress or thermal deformation can be successfully solved. These are convenient for better incorporating the design constraints of various tasks such as injection molded parts, or rapid prototyping and tooling. Mesh generation is the major step of finite element method for n...

The Bank-Holst parallel adaptive meshing paradigm [2, 3, 1] is utilised to solve (1) in a combination of domain decomposition and adaptivity. It can be summarised as follows: Step I Mesh Partition: Starting with a coarse mesh TH , the domain is partitioned into non-overlapping subdomains: Ω = ∪pi=1Ωi. Step II Adaptive Meshing: Each processor i is provided with TH and instructed to sequentially ...

This report presents a mesh adaptation method for higher-order (p > 1) discontinuous Galerkin (DG) discretizations of the two-dimensional, compressible Navier-Stokes equations. The method uses a mesh of triangular elements that are not required to conform to the boundary. This triangular, cut-cell approach permits anisotropic adaptation without the difficulty of constructing meshes that conform...

In this work, we study mesh regularization in Bank-Holst parallel adaptive paradigm when adaptive enrichment in both h (geometry) and p (degree) is used. The paradigm was first introduced by Bank and Holst in [2, 3, 1] and later extended to hp-adaptivity in [5]. In detail, the paradigm can be summarized in the following steps. Step 1 Load Balancing: The problem is solved on a coarse mesh, and a...

We study in this paper a posteriori error estimates for H-conforming numerical approximations of diffusion problems with a diffusion coefficient piecewise constant on the mesh cells but arbitrarily discontinuous across the interfaces between the cells. Our estimates give a global upper bound on the error measured either as the energy norm of the difference between the exact and approximate solu...

Universal meshes have recently appeared in the literature as a computationally efficient and robust paradigm for the generation of conforming simplicial meshes for domains with evolving boundaries. The main idea behind a universal mesh is to immerse the moving boundary in a background mesh (the universal mesh), and to produce a mesh that conforms to the moving boundary at any given time by adju...

We consider fourth order singularly perturbed boundary value problems (BVPs) in one-dimension and the approximation of their solution by the hp version of the Finite Element Method (FEM). If the given problem’s boundary conditions are suitable for writing the BVP as a second order system, then we construct an hp FEM on the so-called Spectral Boundary Layer Mesh that gives a robust approximation...

A new higher-order accurate method is proposed that combines the advantages of the classical p-version of the FEM on body-fitted meshes with embedded domain methods. A background mesh composed by higher-order Lagrange elements is used. Boundaries and interfaces are described implicitly by the level set method and are within elements. In the elements cut by the boundaries or interfaces, an autom...