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## Expressions
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In order to write a differential equation in a mathematical natural way we have developed an expression framework, that allowes exacly this. Instead of adding abstract operator-classes to the problem definition we implement the coefficient functions of the operators using mathematical operators. An example is the following bilinearform
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<!-- begin MathToWeb -->
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<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" title="a(c,\vartheta) := \langle\frac{1}{\epsilon}(\phi^2 - 1) c,\; \vartheta\rangle + \langle\max(10^{-5},\;(\phi+1))\nabla c,\; \nabla\vartheta\rangle ">
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<mrow>
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<mi>a</mi>
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<mo maxsize="1">(</mo>
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<mi>c</mi>
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<mo>,</mo>
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<mi>ϑ</mi>
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<mo maxsize="1">)</mo>
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<mo>:</mo>
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<mo>=</mo>
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<mo>〈</mo>
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<mfrac>
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<mrow>
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<mn>1</mn>
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</mrow>
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<mrow>
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<mi>ϵ</mi>
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</mrow>
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</mfrac>
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<mo maxsize="1">(</mo>
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<msup>
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<mrow>
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<mi>ϕ</mi>
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</mrow>
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<mrow>
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<mn>2</mn>
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</mrow>
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</msup>
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<mo>-</mo>
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<mn>1</mn>
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<mo maxsize="1">)</mo>
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<mi>c</mi>
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<mo>,</mo>
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<mspace width="0.278em"></mspace>
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<mi>ϑ</mi>
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<mo>〉</mo>
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<mo>+</mo>
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<mo>〈</mo>
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<mo>max</mo>
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<mo maxsize="1">(</mo>
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<msup>
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<mrow>
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<mn>10</mn>
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</mrow>
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<mrow>
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<mo>-</mo>
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<mn>5</mn>
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</mrow>
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</msup>
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<mo>,</mo>
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<mspace width="0.278em"></mspace>
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<mo maxsize="1">(</mo>
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<mi>ϕ</mi>
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<mo>+</mo>
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<mn>1</mn>
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<mo maxsize="1">)</mo>
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<mo maxsize="1">)</mo>
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<mo>∇</mo>
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<mi>c</mi>
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<mo>,</mo>
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<mspace width="0.278em"></mspace>
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<mo>∇</mo>
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<mi>ϑ</mi>
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<mo>〉</mo>
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</mrow>
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</math>
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<!-- end MathToWeb -->
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<img src="/uploads/8d0d247b4047613ff6bd9e75afa4ab6d/formula.png" height="50" title="a(c,\vartheta) := \big\langle\frac{1}{\epsilon}(\phi^2 - 1) c,\; \vartheta\big\rangle + \big\langle\max(10^{-5},\;(\phi+1))\nabla c,\; \nabla\vartheta\big\rangle" />
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Assume that φ represents a DOFVector, i.e. a discrete representation of a function in a function-space, that is known in advance, or given by an iterative solution procedure from the last iteration. Here we use a solution component of the problem `prob`:
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