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Finite element approximations of a nonlinear diffusion model with memory |
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| Authors: | Temur Jangveladze Zurab Kiguradze Beny Neta Simeon Reich |
| Affiliation: | 1. Ilia Vekua Institute of Applied Mathematics, Ivane Javakhishvili Tbilisi State University, 2 University Street, 0186, Tbilisi, Georgia 2. Faculty of Exact and Natural Sciences, Ivane Javakhishvili Tbilisi State University, 3 Chavchavdze Ave., 0179, Tbilisi, Georgia 3. Caucasus University, 77 Kostava Ave., 0175, Tbilisi, Georgia 4. Department of Applied Mathematics, Naval Postgraduate School, Monterey, CA, 93943, USA 5. Department of Mathematics, The Technion–Israel Institute of Technology, 32000, Haifa, Israel |
| Abstract: | The convergence of a finite element scheme approximating a nonlinear system of integro-differential equations is proven. This system arises in mathematical modeling of the process of a magnetic field penetrating into a substance. Properties of existence, uniqueness and asymptotic behavior of the solutions are briefly described. The decay of the numerical solution is compared with both the theoretical and finite difference results. |
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