Linear-size nonobtuse triangulation of polygons
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
An accelerated interior point method whose running time depends only on A (extended abstract)
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
An aspect ratio bound for triangulating a d-grid cut by a hyperplane (extended abstract)
Proceedings of the twelfth annual symposium on Computational geometry
Dihedral bounds for mesh generation in high dimensions
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
| Hi-index | 0.00 |
We consider solving an elliptic boundary value problem in the case that the coefficients vary by many orders of magnitude over the domain. A linear finite element method is used. It is shown that the standard method for solving the resulting linear equations in finite-precision arithmetic can give an arbitrarily inaccurate answer because of ill-conditioning in the stiffness matrix. A new method for solving the linear equations is proposed. This method is based on a "mixed formulation" and gives a numerically accurate answer independent of the variation in the coefficients. The numerical error in the soution of the linear system for the new method is shown to depend on the aspect ratio of the triangulation.