This chapter surveys recent numerical advances in the phase field method for geometric
surface evolution and related geometric nonlinear partial differential equations (PDEs) …

We derive a posteriori error estimates for the discretization of the heat equation in a unified
and fully discrete setting comprising the discontinuous Galerkin, various finite volume, and …

We consider the a posteriori error analysis of approximations of parabolic problems based
on arbitrarily high-order conforming Galerkin spatial discretizations and arbitrarily high-order …

In this contribution we present a survey of concepts in localized model order reduction
methods for parameterized partial differential equations. The key concept of localized model …

This work is concerned with the derivation of a robust a posteriori error estimator for a
discontinuous Galerkin (dG) method discretization of a linear nonstationary convection …

This Chapter aims to investigate the error estimation of numerical approximation to a class of
semilinear parabolic problems. More specifically, the time discretization uses the backward …

The aim of this thesis is to derive adaptive methods for discontinuous Galerkin
approximations for both elliptic and parabolic interface problems. The derivation of adaptive …

The main goal of this paper is to obtain error bounds for parabolic integro-differential
equation. The derivation of these bounds is based elliptic and Ritz-Volterra reconstructions …

This work is concerned with the development of a space-time adaptive numerical method,
based on a rigorous a posteriori error bound, for a semilinear convection-diffusion problem …

In this paper, we study a posteriori error estimates for one-dimensional and two-dimensional
linear parabolic equations. The backward Euler method and the Crank–Nicolson method for …