I try to generate a mesh over a region, which has a wavy boundary at its bottom and need very fine mesh around the bottom.

However, the generated mesh boundary is not smooth as the specified region. The region is The generated mesh is If we zone-in we will find the bottom boundary is not ideally smooth and has kinks, see

Anyone know how to generate the meshed boundary as smooth as possible?

The minimum work code is as follows.

Needs["NDSolve`FEM`"];  width = 1; heigth = 0.25; radius = 10;  ydatum = 0.006; Aw = 2 10^-3; [Lambda]w = 0.1; [ScriptCapitalR] =    ImplicitRegion[    Abs[x] <= width/2 && y <= heigth + ydatum &&      y >= x^2/(2 radius) + Aw (1 - Cos[(2 [Pi] x)/[Lambda]w]) +        ydatum, {x, y}]; RegionPlot[[ScriptCapitalR], FrameTicks -> None, PlotPoints -> 20000,   AspectRatio -> Automatic, ImageSize -> Large,   PlotRange -> {{-0.48, 0.48}, {0.005, 0.256}}]  meshrefine =    Function[{vertices, area},     Block[{x, y}, {x, y} = Mean[vertices];      If[ydatum < y < ydatum + 0.01, area > 2.1*10^-7, area > 0.001]]]; mesh1 = ToElementMesh[[ScriptCapitalR], "MeshOrder" -> 1,    MeshRefinementFunction -> meshrefine]  mesh1["Wireframe"]  Show[mesh1["Wireframe"],   PlotRange -> {{-0.025, 0.025}, {0.005, 0.02}}, ImageSize -> 800]