84 citations · 207 across the 15 of their papers we have counts for
14 papers · 1 filter
Coupling of conforming and mixed finite element methods for a model of wave propagation in thermo-poroelasticity in the frequency domain
Hongpeng Li, Cristian Carcamo, Hongxing Rui +1
A dynamic linear thermo-poroelasticity model, containing inertial and relaxation terms with second-order time derivatives, is investigated in this paper. The mathematical and numer…
Improving hp-Variational Physics-Informed Neural Networks for Steady-State Convection-Dominated Problems
Thivin Anandh, Divij Ghose, Himanshu Jain +3
This paper proposes and studies two extensions of applying hp-variational physics-informed neural networks, more precisely the FastVPINNs framework, to convection-dominated convect…
Second order error bounds for POD-ROM methods based on first order divided differences
Bosco García-Archilla, Volker John, Julia Novo
This note proves, for simplicity for the heat equation, that using BDF2 as time stepping scheme in POD-ROM methods with snapshots based on difference quotients gives both the optim…
POD-ROMs for incompressible flows including snapshots of the temporal derivative of the full order solution: Error bounds for the pressure
Bosco García-Archilla, Volker John, Sarah Katz +1
Reduced order methods (ROMs) for the incompressible Navier--Stokes equations, based on proper orthogonal decomposition (POD), are studied that include snapshots which approach the…
Inf-sup stabilized Scott-Vogelius pairs on general simplicial grids for Navier-Stokes equations
Naveed Ahmed, Volker John, Xu Li +1
This paper considers the discretization of the time-dependent Navier-Stokes equations with the family of inf-sup stabilized Scott-Vogelius pairs recently introduced in [John/Li/Mer…
Inf-sup stabilized Scott--Vogelius pairs on general simplicial grids by Raviart--Thomas enrichment
Volker John, Xu Li, Christian Merdon +1
This paper considers the discretization of the Stokes equations with Scott--Vogelius pairs of finite element spaces on arbitrary shape-regular simplicial grids. A novel way of stab…
POD-ROMs for incompressible flows including snapshots of the temporal derivative of the full order solution
Bosco García-Archilla, Volker John, Julia Novo
In this paper we study the influence of including snapshots that approach the velocity time derivative in the numerical approximation of the incompressible Navier-Stokes equations…
Finite element methods respecting the discrete maximum principle for convection-diffusion equations
Gabriel R. Barrenechea, Volker John, Petr Knobloch
Convection-diffusion-reaction equations model the conservation of scalar quantities. From the analytic point of view, solution of these equations satisfy under certain conditions m…
On algebraically stabilized schemes for convection-diffusion-reaction problems
Volker John, Petr Knobloch
An abstract framework is developed that enables the analysis of algebraically stabilized discretizations in a unified way. This framework is applied to a discretization of this kin…
Adaptive Grids in the Context of Algebraic Stabilizations for Convection-Diffusion-Reaction Equations
Abhinav Jha, Volker John, Petr Knobloch
Three algebraically stabilized finite element schemes for discretizing convection-diffusion-reaction equations are studied on adaptively refined grids. These schemes are the algebr…
On reference solutions and the sensitivity of the 2D Kelvin-Helmholtz instability problem
Philipp W. Schroeder, Volker John, Philip L. Lederer +3
Two-dimensional Kelvin-Helmholtz instability problems are popular examples for assessing discretizations for incompressible flows at high Reynolds number. Unfortunately, the result…
Error Analysis of Non Inf-sup Stable Discretizations of the time-dependent Navier--Stokes Equations with Local Projection Stabilization
Javier de Frutos, Bosco García-Archilla, Volker John +1
This paper studies non inf-sup stable finite element approximations to the evolutionary Navier--Stokes equations. Several local projection stabilization (LPS) methods corresponding…
ParMooN - a modernized program package based on mapped finite elements
Ulrich Wilbrandt, Clemens Bartsch, Naveed Ahmed +11
{\sc ParMooN} is a program package for the numerical solution of elliptic and parabolic partial differential equations. It inherits the distinct features of its predecessor {\sc Mo…
Analysis of the grad-div stabilization for the time-dependent Navier-Stokes equations with inf-sup stable finite elements
Javier de Frutos, Bosco García-Archilla, Volker John +1
This paper studies inf-sup stable finite element discretizations of the evolutionary Navier--Stokes equations with a grad-div type stabilization. The analysis covers both the case…