Finite Element Analysis An updated and comprehensive review of the theoretical foundation
of the finite element method The revised and updated second edition of Finite Element …

The analysis of singular perturbed differential equations began early in the twentieth
century, when approximate solutions were constructed from asymptotic expansions …

When using numerical simulation to make a decision, how can its reliability be determined?
What are the common pitfalls and mistakes when assessing the trustworthiness of computed …

The discontinuous Galerkin finite element method (DGFEM) for the time discretization of
parabolic problems is analyzed in the context of the hp-version of the Galerkin method. Error …

Many partial differential equations arising in practice are parameter-dependent problems
that are of singularly perturbed type. Prominent examples include plate and shell models for …

The main purpose of this paper is two-fold: first, to present a critical review of available error-
controlled adaptive finite element methods—with absolute global and goal-oriented error …

We design and analyze several finite element methods (FEMs) applied to the Caffarelli–
Silvestre extension that localizes the fractional powers of symmetric, coercive, linear elliptic …

We consider the bilinear finite element method on a Shishkin mesh for the singularly
perturbed elliptic boundary value problem− ϵ 2 (ι 2u ιx 2+ ι 2u ιy 2)+ a (x, y) u= f (x, y) in two …

In the present paper a survey is given on the application of Shishkin grids to convection‐
diffusion problems with dominant convection, further some new results and open problems …

For the spectral fractional diffusion operator of order 2 s, s∈(0, 1), in bounded, curvilinear
polygonal domains Ω⊂ R 2 we prove exponential convergence of two classes of hp …