fred
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How do I show continuity of the mixed and weak solution to Zaremba problem?
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Step 1. (Construct a lift) Let $H^1_{00}(\Omega)$ denote the subset of $H^1(\Omega)$ that vanishes on the Dirichelet boundary. Let $H^{1/2}_{00}(\partial\Omega)$ denote the set of all traces of ...

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How to apply Lagrange Multipliers to BCs of Time Dependent problems using finite elements?
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In this answer I assume that by finite difference you mean only Forward Euler. Backward Euler and the RK are generalizations of this scheme that I will address at the end of the answer. Like you said ...

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