2. Motivation – Why deal.II?  Adaptive Mesh Refinement (AMR)  Start with solving on coarse grid  Compute error  Refine mesh until error < tolerance  Advantages of AMR  Same accuracy with less cost (uniformly fine meshes are expensive!)  Achieve much higher resolution at areas of interest  Great for solving geophysical problems since the action is localized  Flexibility  C++ program library, not software  Can be written from scratch for complex work  Well documented tutorials www.dealii.orgwww.dealii.org - step 22

3.  Subduction zone is a region where two tectonic plates collide and one sinks beneath the other  Compute mantle flow field and pressure in the interior of Earth at subduction zones by solving Stokes flow equations  This simplified model includes two trapezoidal geometries, each representing the oceanic corner and arc corner  Not coupled – two systems are treated separately  Dip angle of 45° Subduction Model Turcotte and Schubert (2002) Oceanic corner Arc corner

4. Stokes Flow Equations  Non-dimensional model  μ = 1 (uniform viscosity)  b x 2 + b y 2 = 1 (constant plate velocity)  Incompressible flow  No external forces, thus flow is entirely driven by subducting plate velocity (f = 0)  Fluid velocity (u) is set equal to plate velocity (b) on Γ 1  Natural boundary conditions of σ  n = 0 everywhere else

5. Model Geometry Oceanic Corner Arc Corner

6. Weak Formulation

7. Solving with Schur Complement

8. Flow Field in Oceanic Corner

9. Flow Field in Arc Corner

10. Pressure in Oceanic Corner

12. Pressure in Arc Corner

13.  Coupling two sides  Solve stokes flow equations for the “oceanic corner” as previously done  Instead of prescribing a moving wall condition at the ramp (Γ 3 ) of the “arc corner” geometry, set the normal stress at the boundary equal to the external pressure in normal direction, which is obtained from the “oceanic corner” solution “Coupled” Subduction Model

14. Oceanic Corner Arc Corner

15. Flow Field in Arc Corner