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Displaying similar documents to “Analysis and numerical solutions of positive and dead core solutions of singular Sturm-Liouville problems.”

A unified approach to singular problems arising in the membrane theory

Irena Rachůnková, Gernot Pulverer, Ewa B. Weinmüller (2010)

Applications of Mathematics

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We consider the singular boundary value problem ( t n u ' ( t ) ) ' + t n f ( t , u ( t ) ) = 0 , lim t → 0 + t n u ' ( t ) = 0 , a 0 u ( 1 ) + a 1 u ' ( 1 - ) = A , where f ( t , x ) is a given continuous function defined on the set ( 0 , 1 ] × ( 0 , ∞ ) which can have a time singularity at t = 0 and a space singularity at x = 0 . Moreover, n ∈ ℕ , n ≥ 2 , and a 0 , a 1 , A are real constants such that a 0 ∈ ( 0 , ∞ ) , whereas a 1 , A ∈ [ 0 , ∞ ) . The main aim of this paper is to discuss the existence of solutions to the above problem and apply the general results to cover certain classes of singular problems arising in the theory of shallow membrane caps, where we are especially interested...

Improved flux reconstructions in one dimension

Vlasák, Miloslav, Lamač, Jan

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We present an improvement to the direct flux reconstruction technique for equilibrated flux a posteriori error estimates for one-dimensional problems. The verification of the suggested reconstruction is provided by numerical experiments.

A posteriori upper and lower error bound of the high-order discontinuous Galerkin method for the heat conduction equation

Ivana Šebestová (2014)

Applications of Mathematics

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We deal with the numerical solution of the nonstationary heat conduction equation with mixed Dirichlet/Neumann boundary conditions. The backward Euler method is employed for the time discretization and the interior penalty discontinuous Galerkin method for the space discretization. Assuming shape regularity, local quasi-uniformity, and transition conditions, we derive both a posteriori upper and lower error bounds. The analysis is based on the Helmholtz decomposition, the averaging interpolation...

An equilibrated residual method with a computable error approximation for a singularly perturbed reaction-diffusion problem on anisotropic finite element meshes

Sergey Grosman (2006)

ESAIM: Mathematical Modelling and Numerical Analysis

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Singularly perturbed reaction-diffusion problems exhibit in general solutions with anisotropic features, strong boundary and/or interior layers. This anisotropy is reflected in a discretization by using meshes with anisotropic elements. The quality of the numerical solution rests on the robustness of the error estimator with respect to both, the perturbation parameters of the problem and the anisotropy of the mesh. The equilibrated residual method has been shown to provide one of...