feat(thermal): certify shell geometry and local heat operators

include/fesa/elements/thermal_shell.h

@@ -2,26 +2,71 @@
 #define FESA_ELEMENTS_THERMAL_SHELL_H_
 
 #include <array>
-#include <cstddef>
 
+#include "fesa/core/source_identity.h"
+#include "fesa/core/status.h"
 #include "fesa/math/matrix.h"
 #include "fesa/math/vector3.h"
 
 namespace fesa {
 
-/// @brief Local Q4 times two-segment P2 transient-heat shell kernel.
+/// @brief Holds global heat flux at four CCW surface points times six traces.
+/// @note Trace order is -1+, -.5, 0-, 0+, .5, 1-. Frame columns are e1,e2,n.
+struct ThermalShellRecovery {
+  std::array<Vector3, 24> global_flux;
+  std::array<std::array<Vector3, 3>, 4> frames;
+};
+
+/// @brief Owns checked local Q4 times two-segment P2 transient-heat operators.
+/// @note Twenty DOFs are node-major, five stations bottom to top per node.
 class ThermalShell final {
  public:
-  ThermalShell(std::array<std::size_t, 4> node_indices,
-               std::array<Vector3, 4> coordinates, double conductivity,
-               double density, double specific_heat, double thickness);
-  const std::array<std::size_t, 4>& NodeIndices() const noexcept;
+  /// @brief Builds finite consistent capacity/conduction and flux operators.
+  /// @param coordinates Original midsurface Cartesian coordinates, without
+  /// projection.
+  /// @return A complete kernel or a source-identified geometry/material
+  /// failure.
+  static Result<ThermalShell> Create(SourceEntityId source,
+                                     std::array<EntityIndex, 4> node_indices,
+                                     const std::array<Vector3, 4>& coordinates,
+                                     double conductivity, double density,
+                                     double specific_heat, double thickness,
+                                     SourceLocation location = {});
+  /// @brief Returns the original element identity.
+  const SourceEntityId& SourceId() const noexcept;
+  /// @brief Returns Domain node indices, not equation numbers.
+  const std::array<EntityIndex, 4>& NodeIndices() const noexcept;
+  /// @brief Returns the node-major conductivity matrix [power/temperature].
   const Matrix& Conductivity() const noexcept;
+  /// @brief Returns the consistent capacity matrix [energy/temperature].
   const Matrix& Capacity() const noexcept;
+  /// @brief Returns componentwise outward roundoff bounds, excluding quadrature
+  /// error.
+  const Matrix& ConductivityError() const noexcept;
+  /// @brief Returns componentwise outward roundoff bounds, excluding quadrature
+  /// error.
+  const Matrix& CapacityError() const noexcept;
+  /// @brief Evaluates q=-k*grad(T) without averaging the two midsurface traces.
+  /// @return Finite global fluxes and right-handed frames or source-identified
+  /// failure.
+  Result<ThermalShellRecovery> Recover(
+      const std::array<double, 20>& temperature) const;
+
  private:
-  std::array<std::size_t, 4> node_indices_;
+  /// @brief Initializes an unpublished candidate whose operators are filled by
+  /// Create.
+  ThermalShell(SourceEntityId source, std::array<EntityIndex, 4> node_indices,
+               SourceLocation location, double conductivity);
+  SourceEntityId source_;
+  std::array<EntityIndex, 4> node_indices_;
+  SourceLocation location_;
+  double conductivity_value_;
   Matrix conductivity_{20U, 20U};
   Matrix capacity_{20U, 20U};
+  Matrix conductivity_error_{20U, 20U};
+  Matrix capacity_error_{20U, 20U};
+  std::array<std::array<Vector3, 20>, 24> gradients_{};
+  std::array<std::array<Vector3, 3>, 4> frames_{};
 };
 
 }  // namespace fesa