We prove first-order convergence of the semi-explicit Euler scheme combined with a finite element discretization in space for elliptic-parabolic problems which are weakly coupled. This setting includes poroelasticity, thermoelasticity, as well multiple-network models used medical applications. The approach decouples system such that each time step requires solution two small and well-structured...

Highsemiconductor microdisk resonators laterally coupled to optical waveguides serve as compact and robust components in wavelength-division-multiplexing systems. We present an efficient algorithm for the two-dimensional design of wavelength-selective filters based on waveguide-coupled whispering-gallery-mode (WGM) microresonators of arbitrary cross-sectional shape. A full-wave integral equatio...

This work is devoted to prove the exponential decay for energy of solutions a higher order Korteweg–de Vries (KdV)–Benjamin–Bona–Mahony (BBM) equation on periodic domain with localized damping mechanism. Following method in [L. Rosier and B.-Y. Zhang, J. Diff. Equ. 254 (2013) 141–178], which combines estimates, multipliers compactness arguments, problem reduced Unique Continuation Property (UCP...

A parallel fully coupled one-level Newton-Krylov-Schwarz method is investigated for solving the nonlinear system of algebraic equations arising from the finite difference discretization of inverse elliptic problems. Both L and H least squares formulations are considered with the H regularization. We show numerically that the preconditioned iterative method is optimally scalable with respect to ...

Numerous models of industrial processes, such as diffusion in glassy polymers or solidification phenomena, lead to general one phase free boundary value problemswith phase onset. The classicalwell-posedness of a fast diffusion approximation to the concerned free boundary value problems is proved. The analysis is performed via a singular change of variables leading to a singular system in a fixe...

We consider the existence of bound states for the coupled elliptic system ∆u1 − λ1u1 + μ1u 3 1 + βu 2 2u1 = 0 in R n , ∆u2 − λ2u2 + μ2u 3 2 + βu 2 1u2 = 0 in R n , u1 > 0, u2 > 0, u1, u2 ∈ H (R). where n ≤ 3. Using the fixed point index in cones we prove the existence of a five-dimensional continuum C ⊂ R5+ × H (R) × H(R) of solutions (λ1, λ2, μ1, μ2, β, u1, u2) bifurcating from the set of semi...


 We compare four numerical methods for the time discretization of linear coupled elliptic-parabolic systems.
 The monolithic method arising from an implicit Euler is primary solving system.
 Accelerated solution via non-iterative decoupling possible by semi-explicit discretization, using a novel methodology related delay differential equations. For poroelasticity, fixed-stress s...

Novel method for semi-analytical solving of equations a trapped dynamics planetoid m4 close to the plane mutual motion main bodies around each other (in case special type Bi-Elliptic Restricted 4-Bodies Problem) is presented. We consider here three primaries m1, m2, m3 orbiting their center mass on elliptic orbits which are permanently forming Lagrangian configuration an equilateral triangle. O...