Analysis of the L1 scheme for a time fractional parabolic–elliptic problem involving weak singularity

A new algorithm for constructing orthogonal curvilinear grids on a sphere for a fairly general geometric shape of the modeling region is implemented as a “compile-once - use forever” software package. It is based on the numerical solution of the inverse problem by an iterative procedure -- finding such distribution of grid points along its perimeter, so that the conformal transformation of the perimeter into a rectangle turns this distribution into uniform one. The iterative procedure itself turns out to be multilevel - i.e. an iterative loop built around another, internal iterative procedure. Thereafter, knowing this distribution, the grid nodes inside the region are obtained solving an elliptic problem. It is shown that it was possible to obtain the exact orthogonality of the perimeter at the corners of the grid, to achieve very small, previously unattainable level of orthogonality errors, as well as make it isotropic -- local distances between grid nodes about both directions are equal to each other.

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A Time-Dependent Strange Term Arising in Homogenization of an Elliptic Problem with Rapidly Alternating Neumann and Dynamic Boundary Conditions Specified at the Domain Boundary: The Critical Case

Doklady Mathematics ◽

10.1134/s106456242002009x ◽

2020 ◽

Vol 101 (2) ◽

pp. 96-101

Author(s):

J. I. Díaz ◽

D. Gómez-Castro ◽

T. A. Shaposhnikova ◽

M. N. Zubova

Keyword(s):

Boundary Conditions ◽

Elliptic Problem ◽

Critical Case ◽

Domain Boundary ◽

Time Dependent ◽

Dynamic Boundary Conditions ◽

Dynamic Boundary

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Influence of Partial Blocking of the Electrode Surface on the Transfer Coefficients

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc19930496 ◽

1993 ◽

Vol 58 (3) ◽

pp. 496-505

Author(s):

Ondřej Wein

Keyword(s):

Surface Activity ◽

Elliptic Problem ◽

Electrode Surface ◽

Driving Force ◽

Two Dimensional ◽

Transfer Coefficients ◽

Constant Potential ◽

Numeric Solution ◽

Active Zones ◽

Partial Blocking

Partial blocking of the transport surface under the stagnant (nerst) layer is simulated by periodically alternating bands of perfectly insulating zones and active zones with a constant potential of driving force. The numeric solution of the corresponding two-dimensional elliptic problem is represented by a simple empirical correlation for the transfer coefficients. The result is interpreted in terms of a simple electrochemical problem about limiting diffusion currents at electrodes with non-uniform surface activity.

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