Adaptive Mixed Finite Element Methods for Parabolic Optimal Control Problems

<table>The adaptive meshes of the control solution <svg height="7.1624999" id="M365" style="vertical-align:-0.11285pt" version="1.1" viewbox="0 0 7.5374999 7.1624999" width="7.5374999" xmlns="http://www.w3.org/2000/svg">
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<tspan style="font-size: 12.50px; " x="0" y="0">𝑢</tspan>
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</svg> at <svg height="11.1" id="M366" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 51.75 11.1" width="51.75" xmlns="http://www.w3.org/2000/svg">
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<tspan style="font-size: 12.50px; " x="0" y="0">𝑡</tspan>
<tspan style="font-size: 12.50px; " x="7.37677" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="19.417158" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="25.668659" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="28.794409" y="0">2</tspan>
<tspan style="font-size: 12.50px; " x="35.04591" y="0">5</tspan>
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Mathematical Problems in Engineering

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Figure 2

Figure 2: Adaptive Mixed Finite Element Methods for Parabolic Optimal Control Problems 