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PDEs (partial differential equations) are ubiquitous in the modelling of real-world problems. The exact solutions of these equations can never be found in practice, so that numerical schemes (mathematical algorithms executed on a computer) are required for their approximation. The ultimate goal of the RANPDEs project is to design algorithms that allow to compute a numerical approximation with error<\/strong> below some desired tolerance<\/strong> at the expense of minimal computational cost<\/strong>. To this end, we first accurately quantify the overall error and identify its different components:<\/p>\n We then apply adaptivity<\/strong> in a broad sense:<\/p>\n Robust a posteriori error estimators<\/strong> are our main tool. We focus on proofs of contraction<\/strong> and optimality<\/strong> with respect to the total cost of the numerical simulation, for several classes of important model nonlinear partial differential equations<\/strong>. Numerical experiments illustrate all the theoretical developments.<\/p>\n <\/p>","protected":false},"excerpt":{"rendered":" PDEs (partial differential equations) are ubiquitous in the modelling of real-world problems. The exact solutions of these equations can never be found in practice, so that numerical schemes (mathematical algorithms executed on a computer) are required for their approximation. The ultimate goal of the RANPDEs project is to design algorithms\u2026<\/p>\n\n
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