The hp version of the finite element method (hp-FEM) combined with adaptive mesh
refinement is a particularly efficient method for solving PDEs because it can achieve an …

This paper is concerned with near-optimal approximation of a given function $ f\in L_2 ([0,
1]) $ with elements of a polynomially enriched wavelet frame, a so-called quarklet frame …

A framework for performing dynamic mesh adaptation with the discontinuous Galerkin
method (DGM) is presented. Adaptations include modifications of the local mesh step size (h …

We present a new adaptive higher-order finite element method (hp-FEM) for the solution of
boundary value problems formulated in terms of partial differential equations (PDEs). The …

In this article, we develop the a posteriori error estimation of hp–version discontinuous
Galerkin composite finite element methods for the discretization of second‐order elliptic …

An h p-adaptive Discontinuous Galerkin Method for electromagnetic wave propagation
phenomena in the time domain is proposed. The method is highly efficient and allows for the …

In this article we propose a class of so-called two-grid hp-version discontinuous Galerkin
finite element methods for the numerical solution of a second-order quasilinear elliptic …

The aim of this paper is to present a new class of smoothness testing strategies in the
context of h p-adaptive refinements based on continuous Sobolev embeddings. In addition …

In this paper we develop the a posteriori error estimation of hp-adaptive discontinuous
Galerkin composite finite element methods (DGFEMs) for the discretization of second-order …

The first part of the cumulative thesis contains the numerical analysis of different $ hp $-finite
element discretizations related to two different weak formulations of a model problem in …