Some publications concerning the mathematical background of the algorithms implemented in Gascoigne3D.

Error control and adaptivity:

M. Braack, T. Richter
Solutions of 3D Navier-Stokes benchmark problems with adaptive finite elements,
Computers and Fluids, 2006, 35 (4), p. 372-392.

M. Braack, A. Ern
Coupling multimodeling with local mesh refinement for the numerical computation of laminar flames,
Combustion Theory and Modelling, 2004, Vol. 8, Nr. 4, p. 771-788, Bristol.

M. Braack, A. Ern
Adaptive computation of reactive flows with local mesh refinement and model adaptation
Enumath 2003, 159-168, Prague, ed.: Feistauer, Springer 2004

R. Becker, M. Braack
A two-level stabilization scheme for the Navier-Stokes equations
Enumath 2003, 123-130, Prague, ed.: Feistauer, Springer 2004

R. Becker and R. Rannacher
An optimal control approach to a-posteriori error estimation in finite element methods
in Acta Numerica 2001, A. Iserles, ed., Cambridge University Press

M. Braack, A. Ern
A posteriori control of modeling errors and discretization errors
SIAM J. Multiscale Modeling and Simulation, vol. 1, 221-238, 2003

R. Becker and R. Rannacher
A feed-back approach to error control in finite element methods: Basic analysis and examples
 East-West J. Numer. Math., vol. 4, pp. 237-264, 1996


R. Becker, M. Braack
Multigrid techniques for finite elements on locally refined meshes
Numerical Linear Algebra with Applications (Special Issue), 2000, Nr. 7, p. 363-379, Wiley&Sons  


R. Becker, M. Braack
A Finite Element Pressure Gradient Stabilization for the Stokes Equations Based on Local Projections
Calcolo 38 (4), p. 173-199, 2001, Springer Berlin 

M. Braack and E. Burman
Local projection stabilization for the Oseen problem and its interpretation as a variational multiscale method
SIAM J. Numer. Anal., 2006, 43(6), 2544-2566.  

M. Braack, E. Burman, V. John, G. Lube
Stabilized finite element methods for the generalized Oseen problem
Comput. Methods Appl. Mech. Engrg., 2007, 196, 853-866 .

Compressible flows:

M. Braack, R. Rannacher, M. Schmich
A computational study of a splitting scheme for weakly compressible stationary flow

R. Becker, M. Braack
Solution of a stationary benchmark problem for natural convection with high temperature difference
Int. Journal of Thermal Sciences, 41, 2002, p. 428-439 

 Chemical reacting flows:

M. Braack, T. Richter
Stabilized finite elements for 3D reactive flows
Int. J. Numer. Methods Fluids, 2006, 51 (9-10), 981-999.

S. Parmentier, M. Braack, U. Riedel, J. Warnatz
Modelling of combustion in a lamella burner
Combustion Science and Technology, 175, no. 1, 185-206, 2003.

M. Braack, R. Rannacher
Adaptive Finite Element Methods for Low-Mach Number Flows with Chemical Reactions
Lecture Series von Karman Institute, 30th Computational Fluid Dynamics, Vol. 3, 1999, p. 1-93

R. Becker, M. Braack, R. Rannacher
Numerical simulation of laminar flames at low Mach number with adaptive finite elements
Combustion Theory and Modelling, Bristol, 1999, Vol. 3, Nr. 3, p. 503-534 

R. Becker, M. Braack, R. Rannacher, C. Waguet
Fast and Reliable Solutions of the Navier-Stokes Equations Including Chemistry
Computer and Visualization in Science, Nr. 2 and 3, 1999, Springer Berlin 

R. Becker, M. Braack, R. Rannacher
On Error Control for Reactive Flow Problems
Scientific Computing in Chemical Engineering II, Computational Fluid Dynamics, Reaction Engineering, and Molecular Properties, Vol. 1, 1999, p. 320-327, Springer Berlin 

Optimization and Optimal control:

R. Becker, M. Braack, B. Vexler
Numerical parameter estimation for chemical models in multidimensional reactive flows
Combustion Theory and Modelling, 2004, Vol. 8, Nr. 4, p. 661-682, Bristol.

R. Becker, M. Braack, B. Vexler
Parameter identification for chemical models in combustion problems
Appl. Numer. Math., 2005, 54 (3-4), p. 519-536

R. Becker, H. Kapp, R. Rannacher
Adaptive finite element methods for optimal control of partial differential equations: Basic concept
SIAM J. Control Optimization, 2000, Nr. 1, p. 113-132

R. Becker
Mesh adaptation for stationary flow control
J. Math. Fluid Mech, 2001, Vol. 3, Nr. 4, p. 317-341

R. Becker
Mesh Adaptation for Dirichlet Flow Control via Nitsche's method
Comm. in Num. Meth. Engrg., 2002.