1. An application of FEM to the geodetic boundary value problem Z. Fašková, R. Čunderlík Faculty of Civil Engineering Slovak University of Technology in Bratislava, Slovakia

2. Formulation of mixed geodetic BVP Potential theory Geodetic BVP Mixed geodetic BVP Numerical experiments in ANSYS Global Quasigeoid Model

3. Gravity (acceleration) g(x): Gravity (acceleration) g(x): Potential theory - Gravity field Gravity potential W(x): Gravity potential W(x): The Earth

4. Potential theory – Normal field Normal body (equipotential ellipsoid, spheroid) is given by : - major semi axes Normal body (equipotential ellipsoid, spheroid) is given by : - major semi axes a - geopotential coefficient (flattening) - geopotential coefficient J 2,0 (flattening) - geocentric gravitational constant - geocentric gravitational constant GM - spin velocity - spin velocity  Normal potential U(x): Normal potential U(x): Normal gravity  (x) Normal gravity  (x) Ellipsoid

5. Disturbing potential T(x): Disturbing potential T(x): Gravity anomaly  g(x): Gravity anomaly  g(x): Gravity disturbance  g(x) Gravity disturbance  g(x) Potential theory - Disturbing field Ellipsoid

6. Geodetic BVP Height anomaly and geoidal height Height anomaly and geoidal height Stokes-Helmert concept (1849) Stokes-Helmert concept (1849) Molodenskij concept (1960) Molodenskij concept (1960)

7. Mixed geodetic BVP Mixed geodetic BVP  22 The air R1R1 R2R2 

8. Numerical experiments in ANSYS 3D elements (15600 elements) with base 5° * 5°   – 1221 nodes

9. Surface gravity disturbances generated from EGM-96 geopotentential coefficients by using program f477b

10. Potential solution Quasigeoidal heights

11. Comparison of solution with BEM

12. Differences between solutions

13. Thanks for your attention