This paper aims first at a simultaneous axiomatic presentation of the proof of optimal
convergence rates for adaptive finite element methods and second at some refinements of …

A widely used electrostatics model in the biomolecular modeling community, the nonlinear
Poisson–Boltzmann equation, along with its finite element approximation, are analyzed in …

In this paper, an adaptive finite element method for elliptic eigenvalue problems is studied.
Both uniform convergence and optimal complexity of the adaptive finite element eigenvalue …

Adaptive finite element methods (AFEM) are a fundamental numerical instrument in science
and engineering to approximate partial differential equations. In the 1980s and 1990s a …

A residual type a posteriori error estimator is presented and analyzed for Weak Galerkin
finite element methods for second order elliptic problems. The error estimator is proved to be …

We show that optimal mesh refinement algorithms for a large class of PDEs can be learned
by a recurrent neural network with a fixed number of trainable parameters independent of …

Mixed finite element methods with flux errors in H(div)-norms and div-least-squares finite
element methods require a separate marking strategy in obligatory adaptive mesh-refining …

In this paper, we study the mixed finite element method for linear diffusion problems. We
focus on the lowest-order Raviart–Thomas case. For simplicial meshes, we propose several …

In this paper, we prove convergence and quasi-optimal complexity of a simple adaptive
nonconforming finite element method. In each step of the algorithm, the iterative solution of …

It is shown that the $ h $-adaptive mixed finite element method for the discretization of
eigenvalue clusters of the Laplace operator produces optimal convergence rates in terms of …