Analysis of the Block-Grid Method for the Solution of Laplace's Equation on Polygons with a Slit

<table>The highly accurate approximate solution <svg height="22.612499" id="M409" style="vertical-align:-4.7201pt" version="1.1" viewbox="0 0 39.8125 22.612499" width="39.8125" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg> and the exact solution <svg height="7.9499998" id="M410" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 9.2749996 7.9499998" width="9.2749996" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg> in the “singular” part for <svg height="16.049999" id="M411" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 57.950001 16.049999" width="57.950001" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg>, <svg height="11.125" id="M412" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 52.5625 11.125" width="52.5625" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg>.</table>

Abstract and Applied Analysis

fig4

Figure 4

Figure 4: Analysis of the Block-Grid Method for the Solution of Laplace's Equation on Polygons with a Slit 