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 …

We present an algorithm for hp-adaptive collocation-based mesh-free numerical analysis of
partial differential equations. Our solution procedure follows a well-established iterative …

We propose a new practical adaptive refinement strategy for h p-finite element
approximations of elliptic problems. Following recent theoretical developments in …

We design and analyze an adaptive hp-finite element method (hp hp-AFEM) in dimensions
n= 1, 2 n= 1, 2. The algorithm consists of iterating two routines: hp hp-NEARBEST finds a …

This article introduces an hp hp‐adaptive multi‐element stochastic collocation method,
which additionally allows to re‐use existing model evaluations during either hh‐or pp …

The majority of the most common physical phenomena can be described using partial
differential equations (PDEs). However, they are very often characterized by strong …

In this work, we introduce a novel hp-adaptive strategy. The main goal is to minimize the
complexity and implementational efforts hence increasing the robustness of the algorithm …

This paper is concerned with near-optimal approximation of a given univariate function with
elements of a polynomially enriched wavelet frame, a so-called quarklet frame. Inspired by …

For the Poisson problem in two dimensions, we consider the standard adaptive finite
element loop solve, estimate, mark, refine, with estimate being implemented using the p …

In this paper, residual-based a posteriori error estimates for variational inequalities,
including those of the second kind, are proposed. The variational formulation and its …