- Verify existence and uniqueness of solutions to elliptic variational problems;
- Analysis of stablility and regularity of solutions;
- Development of appropriate numerical schemes for elliptic differential equations;
- Prediction of convergence rates and computational costs;
- Efficient implementation of the numerical schemes;
- Interpretation and verification of computed solutions;
- Numerical solution of certain nonlinear problems.
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Sobolev spaces, regularity of solutions, finite element methods, a-priori error analysis,
Strang lemmas, adaptive methods, solution of nonlinear problems.
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