improved…

plate_static.geo
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			element_size = 0.1;
			fine_element_size = element_size;

			Point(1) = {0.5, 0.5, 0, element_size};
			Point(2) = {-0.5, 0.5, 0, element_size};
			Point(3) = {-0.5, -0.5, 0, element_size};
			Point(4) = {0.5, -0.5, 0, element_size};
			Point(5) = {-0.5, 0.001, 0, element_size};
			Point(6) = {0., 0.0, 0, fine_element_size};
			Point(7) = {0.5, 0.0, 0, fine_element_size};
			Point(8) = {-0.5, -0.001, 0, element_size};

			Line(1) = {3, 4};
			Line(2) = {4, 7};
			Line(3) = {7, 1};
			Line(4) = {1, 2};
			Line(5) = {2, 5};
			Line(6) = {5, 6};
			Line(7) = {6, 8};
			Line(8) = {8, 3};

			Line Loop(1) = {1, 2, 3, 4, 5, 6, 7, 8};

			Plane Surface(1) = {1};

			Physical Surface("plate") = {1};

			Physical Line("bottom") = {1};
			Physical Line("right") = {2, 3};
			Physical Line("top") = {4};
			Physical Line("left") = {5,8};