Adaptive finite elements

D. Givoli, J. E. Flaherty, M. S. Shephard. Parallel adaptive finite element analysis of viscous flows based on a combined compressible-incompressible formulation. Int J Numer Meth Heat and Fluid Flow 7 880, 1997. 

V.B. Shenoy et al An adaptive finite element approach to atomic-scale mechanics-the quasicontinuum method. J. Mech. Phys. Solids 47, 611-642 (1999)... 

W.R. Bowen and A.O. Sharif, Adaptive finite element solution of the non-linear Poisson-Boltzmann equation—a charged spherical particle at various distances from a charged cylindrical pore in a charged planar surface, J. Colloid Interface Sci. 187 (1997)... 

Peskin [49] used the Galerkin finite-element method to compute current distribution and shape change for electrodeposition into rectangular cavities. A concentration-dependent overpotential expression including both forward and reserve rate terms was used, and a stagnant diffusion layer was assumed. An adaptive finite-element meshing scheme was used to redefine the problem geometry after each time step. 

Shenoy V. B., Miller R., Tadmor E. B., Rodney D, Phillips R. and Ortiz M., An Adaptive Finite Element Approach to Atomic-Scale Mechanics - The Quasicontinuum Method J. Mech. Phys. Solids AT, 611 (1999). 

Cao, J., and P.K. Kitanidis. 1998b. Adaptive finite element simulation of Stokes flow in porous media. Adv. Water Resour. 22 17-32. 

Y. Song, Y. Zhang, C. L. Baja], and N. A. Baker. Continuum diffusion reaction rate calculations of wild-type and mutant mouse acetylcholinesterase Adaptive finite element analysis. Biophys. J.,... 

The assembly of the multilevel hierarchy depends on the method that discretizes the PBE. Eor ED types of methods, we use so-called multigrid methods The nature of the ED grid lends itself to the assembly of a hierarchy with little additional work. " In the case of adaptive finite element... 

Davis, S. F., Flaherty, J. E., An Adaptive Finite Element Method for Initial-Boundary Value Problems for Parabolic Equation, SIAM J. Sci. Stat. Comput., 3, (1982), 6-27... 

Pepper, D. W., and D. E. Stephenson. 1995. An Adaptive Finite-Element Model for Calculating Subsurface Transport of Contaminant, Ground Water, vol. 33, no. 3, pp. 486-496. 

Reddy, M.P, Schaub, E.G., Reifschneider, L.G., Thomas, H. L. Design and Optimization of Three Dimensional Extrusion Dies Using Adaptive Finite Element, SPE-ANTEC (1999)... 

Braack M. An adaptive finite element method for reactive flow problems. PhD thesis. Heidelberg University 1998. 

EChem++ [9, 14] is based on adaptive finite elements. Both reaction mechanisms and experimental conditions (such as the potential or current program applied to the electrode as an excitation of the electron transfer processes) can flexibly be formulated. It is an open-source program maintaining principles of object-oriented software design [21] and is under continuous development. 

Ludwig K, Morales I, Speiser B (2007) EChem-H- -an object-oriented problem solving envirraunent for electrochemistry. Part 6. Adaptive finite element simulations of controlled-current electrochemical experiments. J Electroanal Chem 608 102-110... 

Harriman K, Gavaghan DJ, Houston P, Kay D, Siili E (2000) Adaptive finite element simulation of currents at microelectrodes to a guaranteed accuracy. ECE and EC2E mechanisms at channel microband electrodes. Electrochem Commun 2 576-585... 

Gavaghan DJ, GiUow K, Suli E (2006) Adaptive finite element methods in electrochemistry. Langmuir 22 10666-10682... 

Harriman K, Gavaghan DJ, Sufi E (2004) Time-dependent EC , ECE and EC2E mechanisms at microdisc electrodes simulation using adaptive finite element methods. J Electroanal Chem 569 35-46... 

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