Taylor-Green order-reduction benchmark in FEniCS, and a remedy (supersedes #650)

README.md

@@ -119,8 +119,8 @@ and grant agreement No 101118139.
 The JU receives support from the European Union's Horizon 2020 research
 and innovation programme and Belgium, France, Germany, and Switzerland.
 This project also received funding from the [German Federal Ministry of
-Education and Research](https://www.bmbf.de/bmbf/en/home/home_node.html)
-(BMBF) grants  16HPC047, 16ME0708 and 16ME0679K. Supported by the European Union - NextGenerationEU. 
+Research, Technology and Space](https://www.bmftr.bund.de/EN/Home/home_node.html)
+(BMFTR) grants  16HPC047, 16ME0708 and 16ME0679K. Supported by the European Union - NextGenerationEU. 
 The project also received help from the [Joint Lab "Helmholtz Information -  Research Software Engineering" (HiRSE)](https://www.helmholtz-hirse.de/).
 
 <p align="center">

pySDC/projects/StroemungsRaum/README.rst

@@ -2,7 +2,7 @@ StroemungsRaum
 ==============
 
 **StroemungsRaum** is a research software project developed within the
-BMBF-funded project
+BMFTR-funded project
 
 *“StrömungsRaum – Novel Exascale Architectures with Heterogeneous Hardware
 Components for Computational Fluid Dynamics Simulations”*
@@ -30,16 +30,38 @@ Implemented examples and test cases include:
 
 - Heat equation
 - Convection–diffusion and nonlinear convection–diffusion problems
-- Incompressible Navier–Stokes equations, using:  
+- Incompressible Navier–Stokes equations, using:
    - Projection methods
    - Monolithic formulations
    - DAE- and PDE sweepers
 
 These serve as benchmarks and demonstrators for scalable space–time CFD
 simulations.
 
+Order reduction from time-dependent boundary conditions
+-------------------------------------------------------
+``run_Navier_Stokes_TaylorGreen_FEniCS.py`` runs a manufactured Taylor–Green
+solution on :math:`[-0.5, 0.5]^2` that is exactly one-periodic in :math:`x` and
+constant on the top and bottom boundary. The *same* solution can therefore be
+computed with time-dependent Dirichlet conditions in :math:`x` or with periodic
+ones, and the difference in the observed temporal order isolates the order
+reduction caused by the time-dependent boundary data alone.
+
+The number of collocation nodes decides whether the effect is visible: RADAU-RIGHT
+with :math:`M` nodes drops from its design order :math:`2M-1` to the stiff order
+:math:`M+1`, so the gap is :math:`M-2` and vanishes for :math:`M = 2`. With
+:math:`M = 4` the measured pressure orders are 7 with periodic and 5 with
+time-dependent Dirichlet conditions.
+
+The third variant, ``differentiated_bc``, imposes the boundary data on its time
+derivative and recovers the stage values by collocation quadrature instead of
+evaluating the data pointwise at the nodes. This is the boundary-condition
+analogue of the differentiated-constraint remedy explored in pull request #641,
+and it removes most of the penalty: at :math:`M = 4` the pressure error drops by
+roughly an order of magnitude, to within a small factor of the periodic case.
+
 Funding
 -------
-Funded by the **German Federal Ministry of Education and Research (BMBF)** under
-grant number **16ME0708**.
+Funded by the **German Federal Ministry of Research, Technology and Space (BMFTR)**
+under grant number **16ME0708**.