Automated mesh adaptation is known to be an efficient way to control discretization errors in
Computational Fluid Dynamics (CFD) simulations. It offers the added advantage that the …

We deal with the goal-oriented error estimates and mesh adaptation for nonlinear partial
differential equations. The setting of the adjoint problem and the resulting estimates are not …

We derive a unified framework for goal-oriented a posteriori estimation covering in particular
higher-order conforming, nonconforming, and discontinuous Galerkin finite element …

In this paper we propose an adjoint-based hp-adaptation method for conservation laws, and
corresponding numerical schemes based on piecewise polynomial approximation spaces …

Partial differential equations (PDE) govern many problems of scientific and engineering
interest. Consequently, numerical solution of PDE has become a key technology in the …

We propose an efficient mesh adaptive method for the numerical solution of time-dependent
partial differential equations considered in the fixed space-time cylinder Ω×(0, T). We employ …

We deal with the numerical solution of linear convection–diffusion–reaction equations using
the h p-variant of the discontinuous Galerkin method on triangular grids. We develop a mesh …

This paper presents a novel, fully computable error approximation and mesh adaptation
approach for functionals defined by second-order elliptic equations. The functionals are …

Abstract Certain Petrov-Galerkin schemes deliver inherently stable formulations of
variational problems on a given mesh by selecting appropriate pairs of trial and test spaces …

This paper applies metric-based mesh adaptation methods to advection-dominated tracer
transport modelling problems in two and three dimensions, using the finite element package …