This paper focuses on developing effective and efficient algorithms for compressing scientific simulation data computed on structured and unstructured grids. A paradigm for lossy compression of this data is proposed in which the data computed on the grid is modeled as a graph, which gets decomposed into sets of vertices which satisfy a user defined error constraint ε. Each set of vertices is replaced by a constant value with reconstruction error bounded by ε. A comprehensive set of experiments is conducted by comparing these algorithms and other state-of-the-art scientific data compression methods. Over our benchmark suite, our methods obtained compression of 1% of the original size with average PSNR of 43.00 and 3% of the original size with average PSNR of 63.30. In addition, our schemes outperform other state-of-the-art lossy compression approaches and require on the average 25% of the space required by them for similar or better PSNR levels.