Relaxed Kačanov Scheme for the -Laplacian with Large Exponent
We introduce a novel relaxed Kačanov scheme for the computation of the discrete minimizer
to the-Laplace problem with. The iterative scheme is easy to implement since each iterate …
to the-Laplace problem with. The iterative scheme is easy to implement since each iterate …
Guaranteed, locally space-time efficient, and polynomial-degree robust a posteriori error estimates for high-order discretizations of parabolic problems
A Ern, I Smears, M Vohralík - SIAM Journal on Numerical Analysis, 2017 - SIAM
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 …
on arbitrarily high-order conforming Galerkin spatial discretizations and arbitrarily high-order …
Adaptive regularization, discretization, and linearization for nonsmooth problems based on primal–dual gap estimators
F Févotte, A Rappaport, M Vohralík - Computer Methods in Applied …, 2024 - Elsevier
We consider nonsmooth partial differential equations associated with a minimization of an
energy functional. We adaptively regularize the nonsmooth nonlinearity so as to be able to …
energy functional. We adaptively regularize the nonsmooth nonlinearity so as to be able to …
A review of recent advances in discretization methods, a posteriori error analysis, and adaptive algorithms for numerical modeling in geosciences
DA Di Pietro, M Vohralík - Oil & Gas Science and …, 2014 - ogst.ifpenergiesnouvelles.fr
Two research subjects in geosciences which lately underwent significant progress are
treated in this review. In the first part, we focus on one key ingredient for the numerical …
treated in this review. In the first part, we focus on one key ingredient for the numerical …
[HTML][HTML] Adaptive asynchronous time-stepping, stopping criteria, and a posteriori error estimates for fixed-stress iterative schemes for coupled poromechanics …
In this paper we develop adaptive iterative coupling schemes for the Biot system modeling
coupled poromechanics problems. We particularly consider the space–time formulation of …
coupled poromechanics problems. We particularly consider the space–time formulation of …
Convergence and quasi-optimal cost of adaptive algorithms for nonlinear operators including iterative linearization and algebraic solver
A Haberl, D Praetorius, S Schimanko… - Numerische Mathematik, 2021 - Springer
We consider a second-order elliptic boundary value problem with strongly monotone and
Lipschitz-continuous nonlinearity. We design and study its adaptive numerical …
Lipschitz-continuous nonlinearity. We design and study its adaptive numerical …
An a posteriori error estimate for vertex-centered finite volume discretizations of immiscible incompressible two-phase flow
In this paper we derive an a posteriori error estimate for the numerical approximation of the
solution of a system modeling the flow of two incompressible and immiscible fluids in a …
solution of a system modeling the flow of two incompressible and immiscible fluids in a …
[HTML][HTML] Adaptive poromechanics computations based on a posteriori error estimates for fully mixed formulations of Biot's consolidation model
This paper is concerned with the analysis of coupled mixed finite element methods applied
to the Biot's consolidation model. We consider two mixed formulations that use the stress …
to the Biot's consolidation model. We consider two mixed formulations that use the stress …
A posteriori error estimates, stopping criteria, and adaptivity for multiphase compositional Darcy flows in porous media
DA Di Pietro, E Flauraud, M Vohralík… - Journal of Computational …, 2014 - Elsevier
In this paper we derive a posteriori error estimates for the compositional model of multiphase
Darcy flow in porous media, consisting of a system of strongly coupled nonlinear unsteady …
Darcy flow in porous media, consisting of a system of strongly coupled nonlinear unsteady …
A posteriori error estimates and stopping criteria for space-time domain decomposition for two-phase flow between different rock types
We consider two-phase flow in a porous medium composed of two different rock types, so
that the capillary pressure field is discontinuous at the interface between the rocks. This is a …
that the capillary pressure field is discontinuous at the interface between the rocks. This is a …