| We develop finite-element and finite-difference methods for boundary value and obstacle problems for the elliptic Heston operator. For the finite-element method we first review existence and uniqueness results for these problems on weighted Sobolev spaces, where their variational formulations are formulated, and finite-dimensional subspaces are chosen to find approximating solutions, and obtain error estimates and numerical results. Similarly, for the finite-difference method, we start by reviewing the existence, uniqueness and regularity results on boundary value and obstacle problems on weighted H older spaces, then consider finite-difference operators, establish discrete maximum principles for them, and obtain error estimates and numerical results. |
