432 citations · 594 across the 35 of their papers we have counts for
12 papers · 1 filter
The crucial role of Lagrange multipliers in a space-time symmetry preserving discretization scheme for IVPs
Alexander Rothkopf, Jan Nordström
In a recently developed variational discretization scheme for second order initial value problems ( J. Comput. Phys. 498, 112652 (2024) ), it was shown that the Noether charge asso…
An SBP-SAT Continuous Galerkin Finite Element Formulation for Smooth and Discontinuous Fields
Arnaud G. Malan, Jan Nordstrom
The high-order accurate continuous Galerkin finite element method offers attractive computational efficiency for computational fluid dynamics. A challenge is however spurious oscil…
A superconvergent stencil-adaptive SBP-SAT finite difference scheme
Viktor Linders, Mark Carpenter, Jan Nordström
A stencil-adaptive SBP-SAT finite difference scheme is shown to display superconvergent behavior. Applied to the linear advection equation, it has a convergence rate $\mathcal{O}(Δ…
A symmetry and Noether charge preserving discretization of initial value problems
Alexander Rothkopf, Jan Nordström
Taking insight from the theory of general relativity, where space and time are treated on the same footing, we develop a novel geometric variational discretization for second order…
Uncertain Data in Initial Boundary Value Problems: Impact on Short and Long Time Predictions
Jan Nordström
We investigate the influence of uncertain data on solutions to initial boundary value problems. Uncertainty in the forcing function, initial conditions and boundary conditions are…
A provably stable and high-order accurate finite difference approximation for the incompressible boundary layer equations
Mojalefa P. Nchupang, Arnaud G. Malan, Fredrik Laurén +1
In this article we develop a high order accurate method to solve the incompressible boundary layer equations in a provably stable manner.~We first derive continuous energy estimate…
Summation-by-parts operators for general function spaces: The second derivative
Jan Glaubitz, Simon-Christian Klein, Jan Nordström +1
Many applications rely on solving time-dependent partial differential equations (PDEs) that include second derivatives. Summation-by-parts (SBP) operators are crucial for developin…
Nonlinear Boundary Conditions for Initial Boundary Value Problems with Applications in Computational Fluid Dynamics
Jan Nordström
We derive new boundary conditions and implementation procedures for nonlinear initial boundary value problems (IBVPs) with non-zero boundary data that lead to bounded solutions. Th…
Encapsulated generalized summation-by-parts formulations for curvilinear and non-conforming meshes
Tomas Lundquist, Andrew Winters, Jan Nordström
We extend the construction of so-called encapsulated global summation-by-parts operators to the general case of a mesh which is not boundary conforming. Owing to this development,…
A method-of-lines framework for energy stable arbitrary Lagrangian-Eulerian methods
Tomas Lundquist, Arnaud Malan, Jan Nordström
We present a novel framework based on semi-bounded spatial operators for analyzing and discretizing initial boundary value problems on moving and deforming domains. This developmen…
Nonlinear Boundary Conditions for Energy and Entropy Stable Initial Boundary Value Problems in Computational Fluid Dynamics
Jan Nordström
We derive new boundary conditions and implementation procedures for nonlinear initial boundary value problems that lead to energy and entropy bounded solutions. A step-by-step proc…
Multi-dimensional summation-by-parts operators for general function spaces: Theory and construction
Jan Glaubitz, Simon-Christian Klein, Jan Nordström +1
Summation-by-parts (SBP) operators allow us to systematically develop energy-stable and high-order accurate numerical methods for time-dependent differential equations. Until recen…