A posteriori error estimates are an important tool to bound discretization errors in terms of computable quantities avoiding regularity conditions that are often difficult to establish. For non-linear and non-differentiable problems, problems involving jumping coefficients, and finite element methods using anisotropic triangulations, such estimates often involve large factors, leading to sub-optimal error estimates. By making use of convex duality arguments, exact and explicit error representations are derived that avoid such effects.

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