Osorio Triana, Eduardo. Finite-difference and finite-element solution of boundary value and obstacle problems for the Heston operator. Retrieved from https://doi.org/doi:10.7282/T3HX1B0K
DescriptionWe develop fi nite-element and fi nite-diff erence methods for boundary value and obstacle problems for the elliptic Heston operator. For the fi nite-element method we fi rst review existence and uniqueness results for these problems on weighted Sobolev spaces, where their variational formulations are formulated, and fi nite-dimensional subspaces are chosen to fi nd approximating solutions, and obtain error estimates and numerical results. Similarly, for the fi nite-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.