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  "body": "\n## Summary\n\nMortar methods are finite element discretizations on a domain cut into subdomains whose meshes need not match across the interfaces.\nContinuity across an interface is not imposed point by point but weakly.\nThe jump must be orthogonal to a space of multiplier functions, the mortar space.\nThey let each subdomain use its own mesh and polynomial degree while keeping optimal error estimates.\nThis makes them a standard tool of [[domain decomposition methods|AN054RHT1K]].\n\n## Explanations\n\n### L1 human\n\nImagine two brick walls built by different masons with bricks of different sizes, which must meet along a seam.\nThe bricks do not line up, so the mortar between them has to absorb the mismatch.\nA mortar method does the same with meshes: two regions are meshed independently, and along their common edge the two sides are glued \"on average\" rather than at every node.\nFor example, a fine mesh around a corner singularity can meet a coarse mesh elsewhere without any transition layer.\n",
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