Research

My research interests include:

• the numerical solution of partial differential equations with finite element and finite volume methods
• a posteriori error estimation and adaptivity
• singular solutions of evolution equations
• scientific computing and visualization

Research grants

• Study of extreme weather phenomena in local regions and their impact to civil protection and the economy. Research Program "SYNERGASIA", Greek Secretariat of Research and Technology, 2011-2013.
• Optimal Managment of Dynamic Systems of the Economy and the Environment. Research Program "THALIS", Section: Social, Administrative and Economical sciences, 2012-2014, Ministry of Education, Lifelong Learning and Religious Affairs. 2012-2014.

Research affiliations

• Institue of Applied and Computational Mathematics, Foundation for Research and Technology, Hellas (FO.R.T.H.)
• Archimedes Center for Modeling, Analysis and Computations (ACMAC).

Publications

• D. A. Mitsoudis, Ch. Makridakis, and M. Plexousakis, Helmholtz Equation with Artificial Boundary Conditions in a Two-Dimensional Waveguide. SIAM J. Math. Anal. 44, (2012), no. 6, 4320-4344. doi: 10.1137/120864052.
• G. Kossioris, M. Plexousakis, A. Xepapadeas and A. de Zeeuw, On the optimal taxation of common-pool resources. J. Econom. Dynam. Control. 35, (2011), no. 11, 1868-1879. doi: 10.1016/j.jedc.2011.05.007.
• N. M. Abukhdeir, D. G. Vlachos, M. Katsoulakis and M. Plexousakis, Long-time integration methods for mesoscopic models of pattern-forming systems. J. Comp. Phys. 230, (2011), no. 14, 5704-5715. doi: 10.1016/j.jcp.2011.03.052.
• I. Kyza, Ch. Makridakis and M. Plexousakis, Error control for time-splitting spectral approximations of the semiclassical Schrödinger equation. IMA J. Numer. Anal. 31, 2011, no. 2, 416-441. doi:10.1993/imanum/drp044.
• Th. Baxevanis, M. Plexousakis, On the effect of fiber creep-compliance in the high-temperature deformation of continuous fiber-reinforced ceramic matrix composites. Intern. J. of Solids and Structures 47, (2010), 2487-2497. doi:10.1016/j.ijsolstr.2010.05.007.
• D. C. Antonopoulou, M. Plexousakis, Discontinuous Galerkin methods for the linear Schrödinger equation in non-cylindrical domains. Numer. Math. 115, (2010), no. 4, 585-608. doi: 10.1007/s00211-010-0296-5.
• D. A. Mitsoudis, M. Plexousakis, A Finite Element Method with Nonlocal Boundary Conditions for the Helmholtz Equation with Complex Wavenumber in Stratified Waveguides. Acta Acustica united with Acustica, 95 (2009), no. 4, 753-756. doi: 10.3813/AAA.918203.
• Th. Baxevanis, M. Plexousakis, Estimation of base settlement from the surface profile: two-dimensional plane field of displacements. Intern. J. for Numer. and Analytical Methods in Geomechanics, 33 (2009), no. 8, 1109-1121. doi: 10.1002/nag.760.
• G. Kossioris, M. Plexousakis, A. Xepapadeas and A. de Zeeuw, Feedback Nash equilibria for non-linear differential games in pollution control. J. Econom. Dynam. Control, 32, (2008), no. 4, 1312-1331. doi: 10.1016/j.jedc.2007.05.008.
• G. Kossioris, M. Plexousakis and A. N. Yannacopoulos, A Hamilton-Jacobi approach to the control of the trapping time of a soliton by an external potential. Quart. Appl. Math. 63, (2005), no. 2, 309-324.
• M. Plexousakis, G. E. Zouraris, On the construction and analysis of high order locally conservative finite volume-type methods for one-dimensional elliptic problems. SIAM J. Numer. Anal. 42, (2004), no. 3, 1226-1260. doi: 10.1137/S0036142902406302.
• P. Chatzipantelidis, Ch. Makridakis and M. Plexousakis, A posteriori error estimates for a finite volume method for the Stokes problem in two dimensions. Appl. Numer. Math. 46, (2003), no. 1, 45-58. doi: 10.1016/S0168-9274(03)00011-4.