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plot_afem.html
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plot_afem.html
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<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
<html><head><meta http-equiv="Content-Type" content="text/html; charset=utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge,IE=9,chrome=1"><meta name="generator" content="MATLAB 2022b"><title>Untitled</title><style type="text/css">.rtcContent { padding: 30px; } .CodeBlock { background-color: #F5F5F5; margin: 10px 0 10px 0; }
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.variableValue { width: 100% !important; }
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.embeddedOutputsMatrixElement .matrixElement .valueContainer .horizontalEllipsis.hide,.embeddedOutputsMatrixElement .matrixElement .verticalEllipsis.hide,.eoOutputWrapper .matrixElement .valueContainer .horizontalEllipsis.hide,.eoOutputWrapper .matrixElement .verticalEllipsis.hide,.rtcDataTipElement .matrixElement .valueContainer .horizontalEllipsis.hide,.rtcDataTipElement .matrixElement .verticalEllipsis.hide { display: none;}
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/* * Ellipses as base64 for HTML export. */.matrixElement .horizontalEllipsis,.rtcDataTipElement .matrixElement .horizontalEllipsis { display: inline-block; margin-top: 3px; /* base64 encoded version of images-liveeditor/HEllipsis.png */ width: 30px; height: 12px; background-repeat: no-repeat; background-image: url("data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB0AAAAJCAYAAADO1CeCAAAAJUlEQVR42mP4//8/A70xw0i29BUDFPxnAEtTW37wWDqakIa4pQDvOOG89lHX2gAAAABJRU5ErkJggg==");}
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.S4 { border-left: 1px solid rgb(191, 191, 191); border-right: 1px solid rgb(191, 191, 191); border-top: 1px solid rgb(191, 191, 191); border-bottom: 1px solid rgb(191, 191, 191); border-radius: 0px; padding: 6px 45px 4px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 14px; }
.S5 { margin: 10px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: rgb(33, 33, 33); font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: left; }</style></head><body><div class = rtcContent><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S0'><span style="white-space: pre"><span >clear</span></span></div></div><div class="inlineWrapper"><div class = 'S1'><span style="white-space: pre"><span >clc</span></span></div></div><div class="inlineWrapper"><div class = 'S1'> </div></div><div class="inlineWrapper outputs"><div class = 'S2'><span style="white-space: pre"><span >A = [2/3 1/3 0; 1/3 4/3 1/3; 0 1/3 2/3]*(pi/4)</span></span></div><div class = 'S3'><div class="inlineElement eoOutputWrapper embeddedOutputsVariableMatrixElement" uid="E58D632E" data-scroll-top="null" data-scroll-left="null" prevent-scroll="true" data-testid="output_0" style="width: 1272px; white-space: normal; font-style: normal; color: rgb(33, 33, 33); font-size: 12px;" data-width="1242"><div class="matrixElement veSpecifier eoOutputContent" style="white-space: normal; font-style: normal; color: rgb(33, 33, 33); font-size: 12px;"><div class="veVariableName variableNameElement double" style="width: 1242px; white-space: normal; font-style: normal; color: rgb(33, 33, 33); font-size: 12px;"><div class="headerElementClickToInteract" style="white-space: normal; font-style: normal; color: rgb(33, 33, 33); font-size: 12px;"><span style="white-space: normal; font-style: normal; color: rgb(33, 33, 33); font-size: 12px;">A = </span><span class="veVariableValueSummary veMetaSummary" style="white-space: normal; font-style: normal; color: rgb(179, 179, 179); font-size: 12px;">3×3</span></div></div><div class="valueContainer" data-layout="{"columnWidth":66,"totalColumns":3,"totalRows":3,"charsPerColumn":10}" style="white-space: nowrap; font-style: normal; color: rgb(33, 33, 33); font-size: 12px;"><div class="variableValue" style="width: 200px; white-space: pre; font-style: normal; color: rgb(33, 33, 33); font-size: 12px;"> 0.5236 0.2618 0
0.2618 1.0472 0.2618
0 0.2618 0.5236
</div><div class="horizontalEllipsis hide" style="white-space: nowrap; font-style: normal; color: rgb(33, 33, 33); font-size: 12px;"></div><div class="verticalEllipsis hide" style="white-space: nowrap; font-style: normal; color: rgb(33, 33, 33); font-size: 12px;"></div></div></div><div class="outputLayer selectedOutputDecorationLayer doNotExport" style="white-space: normal; font-style: normal; color: rgb(33, 33, 33); font-size: 12px;"></div><div class="outputLayer activeOutputDecorationLayer doNotExport" style="white-space: normal; font-style: normal; color: rgb(33, 33, 33); font-size: 12px;"></div><div class="outputLayer scrollableOutputDecorationLayer doNotExport" style="white-space: normal; font-style: normal; color: rgb(33, 33, 33); font-size: 12px;"></div></div></div></div><div class="inlineWrapper outputs"><div class = 'S4'><span style="white-space: pre"><span >B = [(-2+pi)/pi; 4/pi; (-2+pi)/pi]</span></span></div><div class = 'S3'><div class="inlineElement eoOutputWrapper embeddedOutputsVariableMatrixElement" uid="2564FE72" data-scroll-top="null" data-scroll-left="null" prevent-scroll="true" data-testid="output_1" style="width: 1272px; white-space: normal; font-style: normal; color: rgb(33, 33, 33); font-size: 12px;" data-width="1242"><div class="matrixElement veSpecifier eoOutputContent" style="white-space: normal; font-style: normal; color: rgb(33, 33, 33); font-size: 12px;"><div class="veVariableName variableNameElement double" style="width: 1242px; white-space: normal; font-style: normal; color: rgb(33, 33, 33); font-size: 12px;"><div class="headerElementClickToInteract" style="white-space: normal; font-style: normal; color: rgb(33, 33, 33); font-size: 12px;"><span style="white-space: normal; font-style: normal; color: rgb(33, 33, 33); font-size: 12px;">B = </span><span class="veVariableValueSummary veMetaSummary" style="white-space: normal; font-style: normal; color: rgb(179, 179, 179); font-size: 12px;">3×1</span></div></div><div class="valueContainer" data-layout="{"columnWidth":66,"totalColumns":1,"totalRows":3,"charsPerColumn":10}" style="white-space: nowrap; font-style: normal; color: rgb(33, 33, 33); font-size: 12px;"><div class="variableValue" style="width: 68px; white-space: pre; font-style: normal; color: rgb(33, 33, 33); font-size: 12px;"> 0.3634
1.2732
0.3634
</div><div class="horizontalEllipsis hide" style="white-space: nowrap; font-style: normal; color: rgb(33, 33, 33); font-size: 12px;"></div><div class="verticalEllipsis hide" style="white-space: nowrap; font-style: normal; color: rgb(33, 33, 33); font-size: 12px;"></div></div></div><div class="outputLayer selectedOutputDecorationLayer doNotExport" style="white-space: normal; font-style: normal; color: rgb(33, 33, 33); font-size: 12px;"></div><div class="outputLayer activeOutputDecorationLayer doNotExport" style="white-space: normal; font-style: normal; color: rgb(33, 33, 33); font-size: 12px;"></div><div class="outputLayer scrollableOutputDecorationLayer doNotExport" style="white-space: normal; font-style: normal; color: rgb(33, 33, 33); font-size: 12px;"></div></div></div></div><div class="inlineWrapper outputs"><div class = 'S4'><span style="white-space: pre"><span >sol = A\B</span></span></div><div class = 'S3'><div class="inlineElement eoOutputWrapper embeddedOutputsVariableMatrixElement" uid="4578AC8E" data-scroll-top="null" data-scroll-left="null" prevent-scroll="true" data-testid="output_2" style="width: 1272px; white-space: normal; font-style: normal; color: rgb(33, 33, 33); font-size: 12px;" data-width="1242"><div class="matrixElement veSpecifier eoOutputContent" style="white-space: normal; font-style: normal; color: rgb(33, 33, 33); font-size: 12px;"><div class="veVariableName variableNameElement double" style="width: 1242px; white-space: normal; font-style: normal; color: rgb(33, 33, 33); font-size: 12px;"><div class="headerElementClickToInteract" style="white-space: normal; font-style: normal; color: rgb(33, 33, 33); font-size: 12px;"><span style="white-space: normal; font-style: normal; color: rgb(33, 33, 33); font-size: 12px;">sol = </span><span class="veVariableValueSummary veMetaSummary" style="white-space: normal; font-style: normal; color: rgb(179, 179, 179); font-size: 12px;">3×1</span></div></div><div class="valueContainer" data-layout="{"columnWidth":66,"totalColumns":1,"totalRows":3,"charsPerColumn":10}" style="white-space: nowrap; font-style: normal; color: rgb(33, 33, 33); font-size: 12px;"><div class="variableValue" style="width: 68px; white-space: pre; font-style: normal; color: rgb(33, 33, 33); font-size: 12px;"> 0.1148
1.1585
0.1148
</div><div class="horizontalEllipsis hide" style="white-space: nowrap; font-style: normal; color: rgb(33, 33, 33); font-size: 12px;"></div><div class="verticalEllipsis hide" style="white-space: nowrap; font-style: normal; color: rgb(33, 33, 33); font-size: 12px;"></div></div></div><div class="outputLayer selectedOutputDecorationLayer doNotExport" style="white-space: normal; font-style: normal; color: rgb(33, 33, 33); font-size: 12px;"></div><div class="outputLayer activeOutputDecorationLayer doNotExport" style="white-space: normal; font-style: normal; color: rgb(33, 33, 33); font-size: 12px;"></div><div class="outputLayer scrollableOutputDecorationLayer doNotExport" style="white-space: normal; font-style: normal; color: rgb(33, 33, 33); font-size: 12px;"></div></div></div></div></div><div class = 'S5'><span>Plot</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S0'><span style="white-space: pre"><span style="color: rgb(0, 128, 19);">% plot 1</span></span></div></div><div class="inlineWrapper"><div class = 'S1'><span style="white-space: pre"><span >x=0:0.01:pi;</span></span></div></div><div class="inlineWrapper"><div class = 'S1'><span style="white-space: pre"><span >plot(x,sin(x),</span><span style="color: rgb(167, 9, 245);">'DisplayName'</span><span >,</span><span style="color: rgb(167, 9, 245);">'sin(x)'</span><span >,LineWidth=1.5)</span></span></div></div><div class="inlineWrapper"><div class = 'S1'><span style="white-space: pre"><span >hold </span><span style="color: rgb(167, 9, 245);">on</span></span></div></div><div class="inlineWrapper"><div class = 'S1'> </div></div><div class="inlineWrapper"><div class = 'S1'><span style="white-space: pre"><span style="color: rgb(0, 128, 19);">% % plot 2</span></span></div></div><div class="inlineWrapper"><div class = 'S1'><span style="white-space: pre"><span style="color: rgb(0, 128, 19);">% a = pi/2</span></span></div></div><div class="inlineWrapper"><div class = 'S1'><span style="white-space: pre"><span style="color: rgb(0, 128, 19);">% y = x - x.^3/factorial(3) + x.^5/factorial(5) - x.^7/factorial(7) + x.^9/factorial(9);</span></span></div></div><div class="inlineWrapper"><div class = 'S1'><span style="white-space: pre"><span style="color: rgb(0, 128, 19);">% y = sin(a) + (cos(a)).*(x-a) + (-sin(a)).*((x-a).^2)/factorial(2);</span></span></div></div><div class="inlineWrapper"><div class = 'S1'><span style="white-space: pre"><span style="color: rgb(0, 128, 19);">% plot(x,y,'--','DisplayName','Taylor series (a=\pi/2) - 3 terms',LineWidth=1.5)</span></span></div></div><div class="inlineWrapper"><div class = 'S1'><span style="white-space: pre"><span style="color: rgb(0, 128, 19);">% </span></span></div></div><div class="inlineWrapper"><div class = 'S1'><span style="white-space: pre"><span style="color: rgb(0, 128, 19);">% % plot 3</span></span></div></div><div class="inlineWrapper"><div class = 'S1'><span style="white-space: pre"><span style="color: rgb(0, 128, 19);">% y = [];</span></span></div></div><div class="inlineWrapper"><div class = 'S1'><span style="white-space: pre"><span style="color: rgb(0, 128, 19);">% for i=x</span></span></div></div><div class="inlineWrapper"><div class = 'S1'><span style="white-space: pre"><span style="color: rgb(0, 128, 19);">% if i<pi/2</span></span></div></div><div class="inlineWrapper"><div class = 'S1'><span style="white-space: pre"><span style="color: rgb(0, 128, 19);">% y = [y; ((pi/2-i)/(pi/2))*0+((2*i)/(pi))*1];</span></span></div></div><div class="inlineWrapper"><div class = 'S1'><span style="white-space: pre"><span style="color: rgb(0, 128, 19);">% else</span></span></div></div><div class="inlineWrapper"><div class = 'S1'><span style="white-space: pre"><span style="color: rgb(0, 128, 19);">% y = [y; ((pi-i)/(pi/2))*1+((pi/2-i)/(-pi/2))*0];</span></span></div></div><div class="inlineWrapper"><div class = 'S1'><span style="white-space: pre"><span style="color: rgb(0, 128, 19);">% end</span></span></div></div><div class="inlineWrapper"><div class = 'S1'><span style="white-space: pre"><span style="color: rgb(0, 128, 19);">% end</span></span></div></div><div class="inlineWrapper"><div class = 'S1'><span style="white-space: pre"><span style="color: rgb(0, 128, 19);">% plot(x,y,'--','DisplayName','Linear piecewise interpolation',LineWidth=1.5)</span></span></div></div><div class="inlineWrapper"><div class = 'S1'><span style="white-space: pre"><span style="color: rgb(0, 128, 19);">% </span></span></div></div><div class="inlineWrapper"><div class = 'S1'><span style="white-space: pre"><span style="color: rgb(0, 128, 19);">% % plot 4</span></span></div></div><div class="inlineWrapper"><div class = 'S1'><span style="white-space: pre"><span style="color: rgb(0, 128, 19);">% y = (((0-x).*(pi-x))/((0-pi/2)*(pi-pi/2)))*1;</span></span></div></div><div class="inlineWrapper"><div class = 'S1'><span style="white-space: pre"><span style="color: rgb(0, 128, 19);">% plot(x,y,'--','DisplayName','Quadratic lagrange interpolation',LineWidth=1.5)</span></span></div></div><div class="inlineWrapper"><div class = 'S1'> </div></div><div class="inlineWrapper"><div class = 'S1'><span style="white-space: pre"><span style="color: rgb(0, 128, 19);">% plot 5</span></span></div></div><div class="inlineWrapper"><div class = 'S1'><span style="white-space: pre"><span >y = [];</span></span></div></div><div class="inlineWrapper"><div class = 'S1'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">for </span><span >i=x</span></span></div></div><div class="inlineWrapper"><div class = 'S1'><span style="white-space: pre"><span > </span><span style="color: rgb(14, 0, 255);">if </span><span >i<pi/2</span></span></div></div><div class="inlineWrapper"><div class = 'S1'><span style="white-space: pre"><span > y = [y; ((pi/2-i)/(pi/2))*sol(1)+((2*i)/(pi))*sol(2)];</span></span></div></div><div class="inlineWrapper"><div class = 'S1'><span style="white-space: pre"><span > </span><span style="color: rgb(14, 0, 255);">else</span></span></div></div><div class="inlineWrapper"><div class = 'S1'><span style="white-space: pre"><span > y = [y; ((pi-i)/(pi/2))*sol(2)+((pi/2-i)/(-pi/2))*sol(3)];</span></span></div></div><div class="inlineWrapper"><div class = 'S1'><span style="white-space: pre"><span > </span><span style="color: rgb(14, 0, 255);">end</span></span></div></div><div class="inlineWrapper"><div class = 'S1'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">end</span></span></div></div><div class="inlineWrapper"><div class = 'S1'><span style="white-space: pre"><span >plot(x,y,</span><span style="color: rgb(167, 9, 245);">'DisplayName'</span><span >,</span><span style="color: rgb(167, 9, 245);">'L2 projection - linear'</span><span >,LineWidth=1.5)</span></span></div></div><div class="inlineWrapper"><div class = 'S1'> </div></div><div class="inlineWrapper"><div class = 'S1'><span style="white-space: pre"><span style="color: rgb(0, 128, 19);">% plot 6</span></span></div></div><div class="inlineWrapper"><div class = 'S1'><span style="white-space: pre"><span >y = -0.050465 + 1.31224.*x - 0.417697.*x.^2;</span></span></div></div><div class="inlineWrapper"><div class = 'S1'><span style="white-space: pre"><span >plot(x,y,</span><span style="color: rgb(167, 9, 245);">'DisplayName'</span><span >,</span><span style="color: rgb(167, 9, 245);">'L2 projection - quadratic'</span><span >,LineWidth=1.5)</span></span></div></div><div class="inlineWrapper"><div class = 'S1'> </div></div><div class="inlineWrapper"><div class = 'S1'> </div></div><div class="inlineWrapper"><div class = 'S1'><span style="white-space: pre"><span >xlim([0,pi])</span></span></div></div><div class="inlineWrapper"><div class = 'S1'><span style="white-space: pre"><span >ylim([0,2])</span></span></div></div><div class="inlineWrapper"><div class = 'S1'><span style="white-space: pre"><span >daspect([1 1 1])</span></span></div></div><div class="inlineWrapper"><div class = 'S1'><span style="white-space: pre"><span >legend</span></span></div></div><div class="inlineWrapper"><div class = 'S1'><span style="white-space: pre"><span >set(gcf,</span><span style="color: rgb(167, 9, 245);">'units'</span><span >,</span><span style="color: rgb(167, 9, 245);">'pixels'</span><span >,</span><span style="color: rgb(167, 9, 245);">'position'</span><span >,[100 100 1000 700]);</span></span></div></div><div class="inlineWrapper outputs"><div class = 'S2'><span style="white-space: pre"><span >set(gca,</span><span style="color: rgb(167, 9, 245);">'FontSize'</span><span >,15);</span></span></div><div class = 'S3'><img src="data:image/png;base64,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style="height: auto;"></div></div></div>
<br>
<!--
##### SOURCE BEGIN #####
clear
clc
A = [2/3 1/3 0; 1/3 4/3 1/3; 0 1/3 2/3]*(pi/4)
B = [(-2+pi)/pi; 4/pi; (-2+pi)/pi]
sol = A\B
%%
% Plot
% plot 1
x=0:0.01:pi;
plot(x,sin(x),'DisplayName','sin(x)',LineWidth=1.5)
hold on
% % plot 2
% a = pi/2
% y = x - x.^3/factorial(3) + x.^5/factorial(5) - x.^7/factorial(7) + x.^9/factorial(9);
% y = sin(a) + (cos(a)).*(x-a) + (-sin(a)).*((x-a).^2)/factorial(2);
% plot(x,y,'REPLACE_WITH_DASH_DASH','DisplayName','Taylor series (a=\pi/2) - 3 terms',LineWidth=1.5)
%
% % plot 3
% y = [];
% for i=x
% if i<pi/2
% y = [y; ((pi/2-i)/(pi/2))*0+((2*i)/(pi))*1];
% else
% y = [y; ((pi-i)/(pi/2))*1+((pi/2-i)/(-pi/2))*0];
% end
% end
% plot(x,y,'REPLACE_WITH_DASH_DASH','DisplayName','Linear piecewise interpolation',LineWidth=1.5)
%
% % plot 4
% y = (((0-x).*(pi-x))/((0-pi/2)*(pi-pi/2)))*1;
% plot(x,y,'REPLACE_WITH_DASH_DASH','DisplayName','Quadratic lagrange interpolation',LineWidth=1.5)
% plot 5
y = [];
for i=x
if i<pi/2
y = [y; ((pi/2-i)/(pi/2))*sol(1)+((2*i)/(pi))*sol(2)];
else
y = [y; ((pi-i)/(pi/2))*sol(2)+((pi/2-i)/(-pi/2))*sol(3)];
end
end
plot(x,y,'DisplayName','L2 projection - linear',LineWidth=1.5)
% plot 6
y = -0.050465 + 1.31224.*x - 0.417697.*x.^2;
plot(x,y,'DisplayName','L2 projection - quadratic',LineWidth=1.5)
xlim([0,pi])
ylim([0,2])
daspect([1 1 1])
legend
set(gcf,'units','pixels','position',[100 100 1000 700]);
set(gca,'FontSize',15);
##### SOURCE END #####
-->
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