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Error estimates of an efficient linearization scheme for a nonlinear elliptic problem with a nonlocal boundary condition

Marian Slodička — 2001

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We consider a nonlinear second order elliptic boundary value problem (BVP) in a bounded domain Ω dim with a nonlocal boundary condition. A Dirichlet BC containing an unknown additive constant, accompanied with a nonlocal (integral) Neumann side condition is prescribed at some boundary part Γ n . The rest of the boundary is equipped with Dirichlet or nonlinear Robin type BC. The solution is found via linearization. We design a robust and efficient approximation scheme. Error estimates for the linearization...

Recovery of an unknown flux in parabolic problems with nonstandard boundary conditions: Error estimates

Marián Slodička — 2003

Applications of Mathematics

In this paper, we consider a 2nd order semilinear parabolic initial boundary value problem (IBVP) on a bounded domain Ω N , with nonstandard boundary conditions (BCs). More precisely, at some part of the boundary we impose a Neumann BC containing an unknown additive space-constant α ( t ) , accompanied with a nonlocal (integral) Dirichlet side condition. We design a numerical scheme for the approximation of a weak solution to the IBVP and derive error estimates for the approximation of the solution u and...

Error estimates of an efficient linearization scheme for a nonlinear elliptic problem with a nonlocal boundary condition

Marian Slodička — 2010

ESAIM: Mathematical Modelling and Numerical Analysis

We consider a nonlinear second order elliptic boundary value problem (BVP) in a bounded domain Ω N with a nonlocal boundary condition. A Dirichlet BC containing an unknown additive constant, accompanied with a nonlocal (integral) Neumann side condition is prescribed at some boundary part Γ. The rest of the boundary is equipped with Dirichlet or nonlinear Robin type BC. The solution is found linearization. We design a robust and efficient approximation scheme. Error estimates for the...

Div-curl lemma revisited: Applications in electromagnetism

Marián SlodičkaJán Jr. Buša — 2010

Kybernetika

Two new time-dependent versions of div-curl results in a bounded domain Ω 3 are presented. We study a limit of the product v k w k , where the sequences v k and w k belong to Ł 2 ( Ω ) . In Theorem 2.1 we assume that × v k is bounded in the L p -norm and · w k is controlled in the L r -norm. In Theorem 2.2 we suppose that × w k is bounded in the L p -norm and · w k is controlled in the L r -norm. The time derivative of w k is bounded in both cases in the norm of - 1 ( Ω ) . The convergence (in the sense of distributions) of v k w k to the product v w of weak limits...

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