# An hp-adaptive strategy for elliptic problems

## TL;DR

This paper introduces an hp-adaptive method for elliptic problems that intelligently refines the mesh or polynomial degree based on error and smoothness estimates, achieving exponential convergence.

## Contribution

It presents a novel hp-adaptive strategy utilizing refinement history and smoothness estimates for improved convergence in elliptic problems.

## Key findings

- Exponential convergence achieved with the proposed strategy.
- Refinement decisions are guided by a posteriori error and smoothness estimates.
- Numerical experiments validate the effectiveness of the method.

## Abstract

In this paper a new hp-adaptive strategy for elliptic problems based on refinement history is proposed, which chooses h-, p- or hp-refinement on individual elements according to a posteriori error estimate, as well as smoothness estimate of the solution obtained by comparing the actual and expected error reduction rate. Numerical experiments show that exponential convergence can be achieved with this strategy.