The problem of interpolating between discrete fields arises frequently in computational
physics. The obvious approach, consistent interpolation, has several drawbacks such as …

Metric tensors play a key role to control the generation of unstructured anisotropic meshes.
In practice, the most well established error analysis enables to calculate a metric tensor on …

The quasi-static brittle fracture model proposed by G. Francfort and J.-J. Marigo can be Γ-
approximated at each time evolution step by the Ambrosio--Tortorelli functional. In this …

In this paper, we present a new optimal interpolation error estimate in $ L^ p $ norm ($1\leq
p\leq\infty $) for finite element simplicial meshes in any spatial dimension. A sufficient …

In this work we develop an anisotropic a posteriori error analysis of the advection–diffusion–
reaction and the Stokes problems. This is the first step towards the study of more complex …

The anisotropic error indicator presented in [M. Picasso, Comm. Numer. Methods Engrg., 19
(2003), pp. 13--23.] in the frame of the Laplace equation is extended to elliptic and parabolic …

Stabilized finite elements on strongly anisotropic meshes are considered. The design of the
stability coefficients is addressed for both the advection-diffusion and the Stokes problems …

In this paper we derive two a posteriori upper bounds for the heat equation. A continuous,
piecewise linear finite element discretization in space and the Crank–Nicolson method for …

The availability of accurate and efficient numerical simulation tools has become of utmost
importance for the design and optimization phases of existing industrial processes. The …

Mesh adaptation has proven to be very efficient for simulating transient multiphase
computational fluid dynamics applications. In this work, we present a new parallel …