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            <title xml:lang="en">An a posteriori-driven adaptive mixed high-order method with application to electrostatics</title>
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                <term xml:lang="en">a posteriori error analysis</term>
                <term xml:lang="en">variable diffusion</term>
                <term xml:lang="en">discontinuous skeletal methods</term>
                <term xml:lang="en">Discrete Geometric Approach</term>
                <term xml:lang="en">Hybrid High-Order methods</term>
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              <p>In this work we propose an adaptive version of the recently introduced Mixed High-Order method and showcase its performance on a comprehensive set of academic and industrial problems in computational electromagnetism. The latter include, in particular, the numerical modeling of comb-drive and MEMS devices. Mesh adaptation is driven by newly derived, residual-based error estimators. The resulting method has several advantageous features: It supports fairly general meshes, it enables arbitrary approximation orders, and has a moderate computational cost thanks to hybridization and static condensation. The a posteriori-driven mesh refinement is shown to significantly enhance the performance on problems featuring singular solutions, allowing to fully exploit the high-order of approximation.</p>
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