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math.NA2026
A high order accurate and energy stable continuous Galerkin framework on summation-by-parts form for the incompressible Navier-Stokes equations
Mrityunjoy Mandal, Arnaud G Malan, Prince Nchupang +1
This paper presents a high-order accurate Continuous Galerkin Finite Element Method (CGFEM) for solving the initial boundary value problems governed by the Incompressible Navier-St…
math.NA2023
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…
math.NA2023
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…